analyzing data in research

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A power analysis is a statistical procedure needed to determine an effective sample size to make a reasonable conclusion.

Power Analyses (Ali & Bhaskar, 206; Polit & Beck, 2017)

Helps to decide how large a sample is needed to make sure judgments about statistical findings are accurate and reliable.

Prevent the recruitment of too many or too few numbers of subjects.

Must be used to determine sample size before the study begins

Chi-Square is powerful for what it is intended to do – determine if variables are associated in any way.

Chi-Square Analysis (Ali & Bhaskar, 206; Polit & Beck, 2017)

Is a type of inferential statistic.

Evaluates if two categorical variables (e.g., gender, educational level, race, etc.) are related (correlated) in any way.

Appropriate for discrete variables (nominal, ordinal).

Does not work with continuous variables (interval, ratio).

The null hypothesis states that there is no relationship between variables. As such, if the null is accepted, you are agreeing that there is no relationship between variables.

Null Hypothesis Testing (Polit & Beck, 2017)

The beginning point for statistical significance testing.

A formal approach to deciding between two interpretations of a statistical relationship in a sample.

Null Hypothesis – suggests there is no relationship between variables, populations, etc. meaning there was an error in sampling.

Alternative Hypothesis – suggests there is a relationship between variables, populations, etc.

Rejecting the Null Hypothesis – suggests being in support of the Alternative Hypothesis.

I want to pick up on your comments specific to type I and type II error and add some thoughts because it is very important to understand these concepts.

First, I can share that sometimes as a researcher, making sense of a type I and type II error can be really challenging! It is important to understand what each is as well as the strategies researchers use to prevent these errors.

In statistics, a null hypothesis is a statement that one seeks to nullify (that is, to conclude is incorrect) with evidence to the contrary. Most commonly, it is presented as a statement that the phenomenon being studied produces no effect or makes no difference. An example of such a null hypothesis might be the statement, "A diet low in carbohydrates has no effect on people's weight." A researcher usually frames a null hypothesis with the intent of rejecting it: that is, intending to run an experiment which produces data that shows that the phenomenon under study does indeed make a difference (in this case, that a diet low in carbohydrates over some specific time frame does, in fact, tend to lower the bodyweight of people who adhere to it)

A type I error(or error of the first kind) is the incorrect rejection of a true null hypothesis. Usually, a type I error leads one to conclude that a supposed effect or relationship exists when in fact it doesn't. Examples of type I errors include a test that shows a patient to have a disease when in fact the patient does not have the disease, a fire alarm going on indicating a fire when in fact there is no fire, or an experiment indicating that medical treatment should cure a disease when in fact it does not. The type I error rate or significance level is the probability of rejecting the null hypothesis given that it is true. It is denoted by the Greek letter α (alpha) and is also called the alpha level. Often, the significance level is set to 0.05 (5%), implying that it is acceptable to have a 5% probability of incorrectly rejecting the null hypothesis.

Type I error is rejecting the null hypothesis when it is true. This is also known as a false positive finding or conclusion.

A type II error(or error of the second kind) is the failure to reject a false null hypothesis. Examples of type II errors would be a blood test failing to detect the disease it was designed to detect, in a patient who really has the disease; a fire breaking out and the fire alarm does not ring, or a clinical trial of a medical treatment failing to show that the treatment works when really it does. The rate of the type II error is denoted by the Greek letter β (beta) and related to the power of a test (which equals 1−β).

A type II error is the failure of rejecting a false null hypothesis. This is also known as a false negative finding or conclusion.

Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is treated as a statistical impossibility.

sampling.

One of the things that are significant to consider is the use of a sample and sampling error. We all generally understand that a sample, be it randomized or a convenience method, is intended to represent a certain population. Inferences about sample statistics (such as a mean and standard deviation) are used to approximate population parameters. Martin and Bridgmon (2012) posit it is highly unlikely that sample statistics will be exactly the same as population parameters and the difference that emerges is what is referred to as sampling error.

It is important to remember as you move forward in your doctoral program, that the use of random sampling is thought to be the best way to reduce sampling error (Martin & Bridgmon, 2012; Tappen, 2016: Treiman, 2009). However, Shadish et al. (2002) have previously discussed that an alternative selection method to random selection used by experimental researchers is known as purposive sampling. This is an intentional process by a researcher to identify population characteristics, including participants, treatments, outcomes, and settings, and then select a sample that most closely embodies the desired population characteristics. However, I encourage you to carefully consider that random error can occasionally include fluctuations in the characteristics of individuals, such as the motivation level of novice nurses changing rapidly from one intervention to the next. So the timing, or rather, the length of study involving the participants, must always be key part of the methodology design.

Thank you for your post this week that includes an important dialogue about the null hypothesis. As pointed out by MacKenzie et al. (2018), hypothesis testing leads to a dichotomous decision; one either rejects the null hypothesis or not. They also argue the decision by the researcher (to reject or not) can be either right or wrong with respect to the truth. However, it is important to gently remember that a hypothesis can never be “proven” to be correct. I have heard my previous doctoral students describe their findings in this way and this description is inaccurate. We should always be mindful that no amount of experimental testing or evidence can truly prove anything in science (McLaughlin, 2006). Rather, it is important to note that if a research scientist’s results match his/her prediction, then the hypothesis is supported.

The language we use to describe possible problems with a hypothesis is also key. The nomenclature for the errors that can occur, such as Type 1 or Type 2, depend upon the decision of whether to reject the null hypothesis. Other considerations involve the p value and its role in determining to accept or reject the null hypothesis. There are some key factors to remember from the lesson this week on the p value (Taylor, 2019). These include:

With most analyses, an alpha of 0.05 is used as the cutoff for statistical significance;

If the p-value is less than 0.05, we reject the null hypothesis that there is no difference between the means and conclude that a significant difference does exist;

If the p-value is larger than 0.05, we cannot conclude that a significant difference exists;

The p-value is also known as the calculated probability; and

The p-value is commonly referred to as the alpha.

If the null hypothesis is not true, then the effect size will be greater than zero;

The larger the effect size, the greater the degree to which the phenomenon (e.g., the outcome of an intervention study) will be manifested; and

The larger the effect size is, the greater the power will be, so a smaller sample will be needed to detect the phenomenon and reject the null hypothesis (Cohen, 1988) [as cited by Tappen, 2016, p. 128].

I also took particular note of your comments about whether you would utilize the research study with regard to the suggested error. You explained that there are still too many gray areas to feel a comfortable in considering this particular research. I can see certainly see your point about this but want to offer that one of the potential opportunities is for the study to be repeated by other researchers, making note of the contributing factors which contributed to the original sample error. One of the challenges with the case study this week is that the generalizability of the results cannot be considered until the sample error is resolved. Thank you and take care.

the Chi-square test of independence (also known as the Pearson Chi-square test, or simply the Chi square) is one of the most useful statistics for testing hypotheses when the variables are nominal, as often happens in clinical research (McHugh, 2013). Chi Square is used to examine the difference between what you actually find in your study (or DNP Project) and what you are expecting to find. So, there are key questions which should be asked to determine if this test is appropriate for your upcoming DNP Project which include:

Are you trying to see if there is a difference between what you have found and what would be found in a random pattern?

Is the data gathered organized into a set of categories?

In each category, is the data displayed as frequencies (not percentages)?

Does the total amount of data collected (observed data) add up to more than 20?

Does the expected data for each category exceed four?

If any of the answers are no to these questions, then is not the correct test to use. Thanks Angela, and I hope this information is helpful. Take care.

Kindly,

Dr. Kyzar

Reference

McHugh, M.L. (2013). The chi-square test of independence. Biochemia Medica, 23(2), 143-149. http://dx.doi.org/10.11613/bm.2013.018 (Links to an external site.)

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Collapse SubdiscussionKate Blue

Kate Blue

WednesdayJan 27 at 4:56pm

Dr. Kyzar and class,

What statistical procedure is needed to determine an effective sample size to make a reasonable conclusion? Explain your rationale.

When determining the appropriate sample size, the general rule of the have the largest sample size possible is best. This allows for the best representation of the population. Utilizing the power analysis tool helps prevent type II errors or false negatives. In conducting this test, the validity of the conclusion is stronger (Polit, 2016).

Reading through the study, you observe that the researcher used a chi-square analysis to analyze nominal and ordinal data. Is this the appropriate level of statistical analysis to answer the research question? Explain your rationale.

Chi-square analysis determines the differences in variables and is used to test the hypothesis. It can be utilized in both nominal and ordinal data (Chamberlain College of Nursing, 2020). The observed frequencies of outcome following intervention are compared to the expected frequencies of outcome following not intervention. Through calculations, a 0.05 significance is determined. Then the Chi-square value and significance value are compared leading to the p-value, which determines statistical significance. In most nursing research, a value of 0.05 or less is considered to be statistically significant (Polit, 2016).

Reading further, the researcher reports that the p-level led her to conclude that the null hypothesis was rejected. In your critique of the study, you determine that the null hypothesis is true. Do these findings impact your decision about whether to use this evidence to inform practice change? Why or why not?

When the p level is greater than 0.05 it is determined to be not statistically significant. It means more than five out of one hundred times of completing a similar size study the results would show probability of the control versus intervention groups being different by likelihood. If the DNP scholar found a p level less than 0.05 it would be considered statistically significant and support the null hypothesis (Polit, 2016).

When a researcher rejects a null hypothesis that is true a type 1 error occurs. When the criteria for type 1 is very tight there is a higher chance for type 2 errors. To avoid type 2 errors the researcher wants to have a larger sample size. This would change the DNP scholar’s choice to utilize in practicum. When there is an error it may be related to inadequate sample size, poor statistical processes, inaccurate measures, or errors in the study method (Polit, 2016). Therefore, the level of evidence would be poor leading to a non-acceptable study for implementing practice change.

References

Chamberlain College of Nursing. (2020). NR 714 Week 4: Data Analysis [Online lesson]. Adtalem Global Education.

Polit, D. F. (2016). Nursing research: Generating and assessing evidence for nursing practice (10th ed.). Wolters Kluwer Health.

Excellent comments to this week’s post! You have provided a highly competent discussion of the Week 4 questions and I took particular note of your points about the Chi Square Analysis. Since this is one of the main focuses of our study this week, I want to summarize some very important key points about this important test. Below are a list of advantages and disadvantages that students should remember.

Advantages

Noted for its robustness with respect to distribution of the data and ease of computation;

The detail of information which can be derived from the test;

It use in studies when certain parametric assumptions cannot be met;

Its flexibility in handling data from both two groups and multiple group studies;

Can be used to test the difference between an actual sample (actual data) or observed, and hypothetical expectations (expected outcome/values from a hypothesis);

Can test association between variables;

Used to test the difference between what you expect to find from an experiment, and what you actually find from an experiment; and

Examines the differences in data between categories.

Disadvantages

Can be used on raw data that is counted (BUT cannot be used for measurements, proportions, or percentages);

Data must be numerical;

Categories of two are not good to compare;

The number of observations must be 20+;

The test becomes invalid if any of the expected values are below 5; and

A type of nonparametric statistics and is not as powerful as other types of statistical methods.

Thanks so much and I hope this information greatly adds to your knowledge this week about this important test.

Kindly,

. Additionally an estimate of a sample size is used to avoid a type 2 error which happens when the null hypothesis is accepted when it should be rejected (Polit & Beck, 2017, p 402).

These comments are at the heart of a power analysis, which is a method of estimating that the sample is large enough to assume that your statistical analysis is meaningful and large enough to detect errors. An underpowered quantitative study typically has too few subjects or an insensitive measure of change (or both), leading to an increased risk of type 2 errors. The effect size is another important estimate of power and is the estimated magnitude of the phenomenon under study (Tappen, 2016, p. 127). Consider then, that if the null hypothesis is true, the effect size will be zero; however, most researchers anticipate a real effect in most of their studies. Thus, it is important for the researcher to actually conduct a real calculation of the sample population which will be needed.

I can share that there are some very useful software packages that can calculate power for you (many are free on the internet), but some of these may be limited by the number of designs that can be inputted into the calculation in question (Creswell & Creswell, 2017). Ultimately, the best advice for doctoral students and novice researchers is to use as large of a sample as possible to maximize the possibility that the means, percentages, and other statistics are the true estimates of the population (Wood & Ross-Kerr, 2011, p. 129

Please click on the link below and read the brief discussion. Knowing the content this week may be a bit challenging, does the illustration help solidify your understanding of rejecting the null hypothesis (meaning a difference exists) or failing to reject the null (meaning no difference was found)?

Best Regards,

Dr. Kyzar

https://www.statisticssolutions.com/to-err-is-human-what-are-type-i-and-ii-errors/ (Links to an external site.)

Rejecting the Null Hypothesis--Week 4.jpg

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Collapse SubdiscussionCarlos Legra Elias

Carlos Legra Elias

SaturdayJan 30 at 12:55pm

Hi Dr Kyzar

Excellent to know how rejecting and failing to reject null hypothesis The illustration explains the concept of Type I and Type II error that can result from rejecting and failing to reject the null hypothesis (Davis, 2020). Type I error occurs when a true null hypothesis is rejected. Type II error on the side occurs when we fail to reject a false hypothesis. The rejection region as illustrated depends on the significant level provided. A significant level of α = 0.05 is commonly used in many research studies. However, other significant levels such as α = 0.01 and α = 0.10 can also be used depending on the requirement and type of the study. Using one of the significant levels affects the decisions made on the null hypothesis. A calculated p-value can be statistically significant when α = 0.10 but fails to be significant when the significant level is changed to α = 0.05.

This study helps in illustration of hypotheses testing during data analysis. This is one of the most vital part that can lead to decision making using the provided data. It is clear from the given illustration that decisions made have a great impact and the type of error committed can be costly depending on the study at hand. This explains the importance of keenness when handling hypotheses.

Therefore, the article solidifies the understanding of rejecting the null hypothesis and failing to reject the null hypothesis. It helps in understanding how irrelevant a decision can be when either of the errors is made.

Reference

Davis, I. (2020, March 4). To Err is Human: What are Type I and II Errors? Retrieved January 30, 2021, from https://www.statisticssolutions.com/to-err-is-human-what-are-type-i-and-ii-errors/ (Links to an external site.)

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Collapse SubdiscussionJannet Patton

Jannet Patton

SaturdayJan 30 at 8:34pm

Greetings, Dr. Kyzar and Class,

Thank you for providing the additional resources and questions this week to further our understanding of Type I and Type II errors. I especially appreciated the article from Statistics Solutions and the illustration about holding versus looking at puppies to demonstrate the difference between a Type I and Type II error. For example, if a researcher rejects a true null hypothesis, this would be a Type I error-also known as a false-positive. If the researcher fails to reject a false null hypothesis, this would be considered a false-negative result (McLeod, 2019). Type I errors can cause unnecessary problems when making healthcare changes, and Type II errors can prevent needed interventions (McLeod, 2019). I have attached a visual chart that demonstrates the conclusion from statistical analysis, based on whether the results yielded a Type I error or Type II error (McLeod, 2019).

Jan

Reference

McLeod, S. A. (2019). What are type I and type II errors? Simple Psychology. https://www.simplypsychology.org/type_I_and_type_II_errors.html (Links to an external site.)

McLeod_Chart.docx

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Collapse SubdiscussionRacheal Aneke

Racheal Aneke

WednesdayJan 27 at 9:19pm

NR 714 week 4 discussion

What statistical procedure is needed to determine an effective sample size to make a reasonable conclusion? Explain your rationale.

To determine if the sample size is adequate to make a reasonable decision depends on the descriptive statistics applied in the study like mode, median, and mean. Mode occurs with the most significant mathematical values frequency and measures the nominal data in a central tendency. The median score is at the 50th percentile or center of the frequency or distribution. It is the correct measurement of the ordinal data. Mean is the sum of the total score divided; it measures the interval and ratio. Another statistical method to decide a sample size includes the range, variance, and standard deviation. Chi-test is also a statistical procedure that is needed to determine sample size (Chamberlain College of Nursing. (2021). Facts remain that there might be enough participants in a research study and statistical methods to select the sample size. The sample size in quantitative research studies is sometimes invariable, numerical at the beginning of the study, or the end as a narrative (Gray & Grove, 2021). One numerical technique does not decide a sample size in a study.

Reading through the study, you observe that the researcher used chi-square analysis to analyze nominal and ordinal data. Is this the appropriate level of statistical analysis to answer the research question? Explain your rationale.

The Chi-square test is the statistical procedure that describes the different variables in a research study, such as if they are dependent or independent variables. It determines the descriptive measurements and can use nominal or ordinal data, but not for causalities. Since this is the case, the Chi-square analysis is acceptable to use to answer the research question. Chi-square results are not significant if there is no difference in the outcome, but the researcher using chi-square implement numerous samples (Chamberlain College of Nursing, 2021). But if the product is positive, it is applied. My research question can be answered with chi-square because it assesses the mentally ill in a crowded environment.

Type II error regarding null hypotheses occurs because of mistakes in the research methods, but they are false positives. Type II error risk is decided using power analysis. Power analysis includes the level of significance, sample size, power, and effect size as parameters (Polit & Beck, 2017). As long as the minimum power level is obtained for the study, the validity is more robust, and the study is less questionable. Based on the fact that if a research null hypothesis is rejected, the power level analysis is reported to question the study's outcome validity, I would not change my decision to use it as evidence to inform practice change.

References

Chamberlain College of Nursing. (2021). NR-714 week 3: Summaries of multiple Research studies Address the Systematic Review.[Online lesson]. Adtalem Global Education.

Gray, J., & Grove, S. K. (2021). Burns and Grove's the practice of nursing research: appraisal, synthesis, and generation of evidence. Elsevier.

Polit, D. F., & Beck, C. T. (Eds.). (2017). Nursing research: Generating and assessing

evidence for nursing practice (10th ed.). Wolters Kluwer. 

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Collapse SubdiscussionTheresa Kyzar

Theresa Kyzar

FridayJan 29 at 6:17pm

Hi Racheal:

Thank you for your practical commentary to the Week 4 discussion. I noted the macro-level perspective you provided as part of a general overview of statistical methods and the chi square test. However, I want you to take a deeper dive with me because it is important to really grasp the concepts associated with parametric and non-parametric testing. Remember that you will likely be required during your defense presentation of your DNP project to discuss your data analysis to demonstrate mastery of the statistical tests you utilized to measure the outcomes of your change project. It will be exciting, I promise!

So, let’s talk about this more at the doctoral level now so you will be able to explain it during your final DNP Project presentation. As you have learned from your assigned chapter readings this week, the Chi-square test is a non-parametric statistic, also called a distribution free test (Polit & Beck, 2017). From this important information, you (and your fellow student peers) have learned that non-parametric tests should be used when any one of the following conditions pertains to the data:

The level of measurement of all the variables is nominal or ordinal.

The sample sizes of the study groups are unequal; for the χ2 the groups may be of equal size or unequal size whereas some parametric tests require groups of equal or approximately equal size.

The original data were measured at an interval or ratio level, but violate one of the following assumptions of a parametric test:

The distribution of the data was seriously skewed or kurtotic (parametric tests assume approximately normal distribution of the dependent variable), and thus the researcher must use a distribution free statistic rather than a parametric statistic.

The data violate the assumptions of equal variance or homoscedasticity.

For any of a number of reasons, the continuous data were collapsed into a small number of categories, and thus the data are no longer interval or ratio (McHugh, 2013).

Sometimes the term, homoscedasticity, scares students, but really it shouldn’t. It just means “having the same scatter”. As an example, we want our data results from the participant responses to a questionnaire used as part of a DNP project or research study to be scattered evenly on a plot graph. This is very important if I am trying to compare the responses between two groups who participated (such as physician responses vs nurse responses). However, both groups need to be the same sample size or interpretation of the data, especially for comparison, could be compromised. Does that make sense? Look at the example below:

Homoscedasticity Example.jpg

What about Groups B & C? Is it the same, meaning, evenly scattered? The answer is no, likely because the two groups in the project were not the same sample size (say as an example, 10 nurse and 6 physician participants). So, I cannot say determine an association in the data (among participant responses) and that is a problem. This is where the important use of non-parametric testing comes into play and I will likely need to use a chi square test analysis. The exciting aspect of this particular test is its flexibility in handling data from both two groups and multiple group studies and I can then delve into a possible association between the two sample groups.

Does this information help to better explain how nonparametric testing, including a chi square test can support your upcoming DNP project data analysis? Let me know your thoughts. Thanks!

Kindly,

Dr. Kyzar

References

McHugh, M.L. (2013). The chi-square test of independence. Biochemia Medica, 23(2), 143-149. http://dx.doi.org/10.11613/bm.2013.018 (Links to an external site.)

Ogee, A., Ellis, M., Scibilia, B., & Pammer, C. (2021). Homoscedasticity? Don't be a victim of statistical hippopotomonstrosesquipedaliophobia. https://blog.minitab.com/blog/statistics-and-quality-data-analysis/dont-be-a-victim-of-statistical-hippopotomonstrosesquipedaliophobia (Links to an external site.)

Polit, D. F., & Beck, C. T. (2017). Nursing research: Generating and assessing evidence for nursing practice (10th ed.). Wolters Kluwer.

, R. (2016). Advanced nursing research: From theory to practice (2nd ed). Jones & Bartlett.

Edited by Theresa Kyzar on Jan 29 at 6:21pm

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Collapse SubdiscussionRacheal Aneke

Racheal Aneke

SundayJan 31 at 8:36am

Dr. Kyzar,

Thank you so much for those in-depth explanations on how to solve homoscedasticity problems with non-parametric testing like chi-square.

Yes, it was and will be more helpful on this DNP Journey.

I appreciate your support,

Racheal Aneke

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Collapse SubdiscussionKimberly Austin

Kimberly Austin

ThursdayJan 28 at 5:36pm

As a practice scholar, you are searching for evidence to translate into practice. In your review of evidence, you locate a quantitative descriptive research study as possible evidence to support a practice change. You notice the sample of this study includes 200 participants and is not normally distributed. Reflect upon this scenario to address the following.

What statistical procedure is needed to determine an effective sample size to make a reasonable conclusion? Explain your rationale.

Research typically relies on samples for their data. Because of the importance of the accuracy of data collected, researchers must carefully choose their samples. Samples should allow the researchers to draw conclusions with good validity and pertain beyond the sample used (Polit & Beck, 2017).

A sampling plan identifies how subjects are selected and how many subjects should be used for the research. In the first step, researchers should clearly identify the criteria that defines who is in the population, and if it represents all types of individuals and diversity for similarly occurring circumstances. This eligible criteria composes the inclusion or exclusion criteria needed for the study. Additional considerations should include costs, constraints, individual ability to participate, and design considerations (Polit & Beck, 2017).

The statistical procedure needed to determine an effective sample size is power analysis. Power analysis is best used with larger sample groups to decrease the likelihood of achieving a deviant sample (Polit & Beck, 2017). In the scenario above, the study includes 200 participants therefore power analysis would be best for this quantitative study as this sample will have an increased likelihood of being representative, however the large sample does not guarantee this (Polit & Beck, 2017).

The Chi-Square Test determines if two variables are independent or related. This case is typically used with nominal or ordinal data, and results used when the analysis shows a difference (Chamberlain, 2020).

According to McHugh (2013) the Chi-square test is a non-parametric statistic, or distribution free, test, therefore is appropriate for use in the study reviewed above.

Polit and Beck (2017) explain that hypothesis testing is based on negative inference. When differences occur from random factors, it is known as the null hypothesis. When this occurs, care must be taken to not jump to quickly on how to use these results. When deciding to accept or reject a null hypothesis, researchers, must determine how probable that chance was the factor causing the results. Rejecting a true hypothesis, or accepting a false hypothesis are two types of statistical errors researchers can make, known as Type I and Type II errors (Polit & Beck, 2017).

In the scenario above, the researcher concluded the null hypothesis was rejected, however upon my further review, the null hypothesis is true, therefore the researcher made a Type I error; and I would use these findings to support the practice change.

References

Chamberlain College of Nursing. (2020). NR 714 Week 4: Data Analysis [Online lesson]. Adtalem Global Education.

McHugh M. L. (2013). The chi-square test of independence. Biochemia medica, 23(2), 143–149. https://doi.org/10.11613/bm.2013.018

Polit, D. F., & Beck, C. T. (2017). Nursing research: Generating and assessing evidence for nursing practice (10th ed.). Wolters Kluwer Health.

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Collapse SubdiscussionKayla Jones

Kayla Jones

SundayJan 31 at 12:10pm

Hi Kimberly,

Thank you for further explanation in simplest terms for this week’s discussion! Dreaded by statistics, it has been insightful to review the readings in detail along with reading everyone’s posts! While many of us may not communicate the statistical terminology in talking to others, it is used in our everyday life. Hypotheses are basically our guesses of why and how events are occurring. In many instances, our guesses are inspired by our beliefs and experiences (Kaur, 2017). However, in research the hypothesis is the relationship between the independent and dependent variable. The independent variable is the cause with the dependent variable being the effect. Hypotheses play a different role in qualitative and quantitative research. Quantitative research stimulates critical thinking, engaging the researcher to interpret the data. Qualitative research usually does not include the hypothesis in the early stages because observation and detailed interviews/inquiries are the driving forces to justify the hypothesis (Kaur, 2017). Concluding the research, a significance level is established to test the hypothesis in which can further determine the reliability. In agreement with you, it is my belief that it would be safe to implement the change.

Reference

Kaur, S. P. (2017). Writing the hypothesis in research. International Journal of Nursing Education, 9(3), 122-125. https://doi:10.5958/0974-9357.2017.00081.2Links to an external site.

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Collapse SubdiscussionTheresa Kyzar

Theresa Kyzar

SundayJan 31 at 6:26pm

Hi Kim,

Thank you for your contribution to the week 4 discussion!

A key point to remember from this discussion relates to power analysis. Please allow me to build on your post.

A power analysis is a statistical procedure needed to determine an effective sample size to make a reasonable conclusion. Researchers conduct a power analysis before recruiting human subjects into their quantitative research study. In each published quantitative study, the research team will state a power analysis as well as report what it was a priori.

Power Analyses (Ali & Bhaskar, 2016; Polit & Beck, 2021)

Help decide how large a sample is needed to make sure judgments about statistical findings are accurate and reliable.

Prevent the recruitment of too many or too few numbers of subjects.

The cut-off for a power analysis is 0.80.

Must be used to determine sample size beforethe study begins

Thank you and take care.

Kindly,

Dr. Kyzar

References

Ali, Z., & Bhaskar, S. B. (2016). Basic statistical tools in research and data analysis. Indian Journal of Anesthesia, 60(9), 662–669. doi:10.4103/0019- 5049.190623. Retrieved https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5037948/ (Links to an external site.).

Polit, D.F. & Beck, C. T. (2021). Nursing research: Generating and assessing evidence for nursing practice (11th ed). Wolters Kluwer.

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Collapse SubdiscussionCarlene Yearwood

Carlene Yearwood

ThursdayJan 28 at 8:49pm

Dr. Kyzar and class,

With regards to the sample size of 200 participants and not normally distributed, the statistical procedure needed to determine an effective sample size for a reasonable conclusion is the P value or alpha level, power analysis, effect and alternative hypothesis. Sample size is a critical step in the design of a well - planned research protocol (Polit & Beck, 2017). P values states whether an observation is as a result of a change made or random occurrences. In order to accept the result there must be a low - p value. Studies must have an adequate sample size, relative to the goals and variabilities of the study (Suresh, et, al. 2012).

Chi- square analysis is used to analyze nominal and ordinal data. The chi- square test analysis is one of the most useful statistics for testing hypotheses when the variables are nominal in clinical research (Mc Hugh, 2013). This is the appropriate level of statistical analysis to answer the research question since chi- square can provide information not only on the significance of any observed differences, but also provides detailed information on exactly which categories account for any differences found. The amount and detail of information this statistical analysis can provide makes it one of the most useful tools available to researchers for analysis ( Mc Hugh, 2013).

Depending on the p - value, a low p - value means the sample result would be unlikely if the hypothesis were true and leads to the rejection of the null hypothesis. In null hypothesis testing the criterion is called a (alpha) and is almost set to .05. If there is enough evidence to conclude that the null hypothesis is true, I will use the evidence to inform practice change. Researchers can only conclude that hypotheses are probably true or false and there is always a risk for error ( Polit & Beck, 2017). Researchers can make a Type 1 error by rejecting a null hypothesis that is true.

References

Mc Hugh, M., L. ( 2013). The Chi - square test of independence. Biochemia Medica, 23 ( 2), 143 - 149.

Polit, D.F. & Beck, C. T. (2017). Nursing research: Generating and assessing evidence for nursing practice (10th ed.). Wolters Kluwer.

Suresh, K. P. & Chandrashekara, S. (2012). Sample size estimation and power analysis for clinical research studies. Journal of Human Reproductive Sciences, 5 ( 1), 7 - 13.

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Collapse SubdiscussionEjiro Ohonbamu

Ejiro Ohonbamu

SundayJan 31 at 7:25pm

Carlene thanks for your post. In other to get a better understanding, of the p-value. You stated that the researchers can make a Type 1 error by rejecting a null hypothesis which is true. The null hypothesis in many types of research is typically not voiced, but in this case, it is. Now to determine the obvious that the null was actually true. The null hypothesis is truthfully based on statistical errors that precede further investigation. Prior to any conclusion, do you not think that what led to the initial rejection must be investigated? Will you be using the evidence for the rejection to inform the practice change? I am thinking that the evidence that led to the rejection, is the same evidence that has led to the truth. The higher the level of significance, the more extreme, nature of the risk of a Type I error diminishes (Polit & Beck, 2017). Thanks for your post.

References

Polit, D. F., & Beck, C. T. (Eds.). (2017). Nursing research: Generating and assessing

evidence for nursing practice (10th ed.). Wolters Kluwer. 

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Collapse SubdiscussionTheresa Kyzar

Theresa Kyzar

ThursdayJan 28 at 10:01pm

Week 4 Class Question

Students:

What is a normal distribution and what does it look like? Why is the normal distribution important in statistics?

I look forward to your responses. Thank you!

Dr. Kyzar

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Collapse SubdiscussionAngela Wilson

Angela Wilson

FridayJan 29 at 2:30pm

Dr. Kyzar and class,

A normal distribution looks like a bell curve. The normal distribution is used in statistics to describe how the variables are distributed in the research study. This is especially significant in evaluating whether the values from the variables are reliable and significant to the research question. Understanding the normal distribution can assist with the evaluation of whether the study is worth translating into practice. The bell curve can show the normal, medium, and mean of the statistical data gathered from the study. Averages can be calculated as well. The bell curve also shows a relationship between the results of the interventions in a study. For example, the tails of the distribution should be equal to the peak in the distribution to determine that both variables are just as likely as the next. This is extremely useful in deciding if the results from the study meet the specifics of the practice setting seeking evidence based practice improvements.

Angie

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Collapse SubdiscussionKimberly Austin

Kimberly Austin

SundayJan 31 at 12:30pm

Angie,

In your post, you mention "the bell curve also shows a relationship between results of the interventions in a study". As I picture this, what comes to mind is something very different than what I used to picture when interpreting data. Since the last time I took a statistics class, our world has changed; and looking at a "curve" or the phrase, "flattening the curve" has become much more well-known since the beginning of the Covid-19 pandemic. Identifying the relationship between results of the interventions has taken on great importance to more than just scientists and scholars as the world tries to understand what is happening with the spread of the Covid-19 virus. In an interesting twist, seeing normal distribution exampled in relationship to Covid-19 has helped me better understand a concept I have struggled with in the past. I appreciate your post in further clarifying the usefulness in determining how results can be applied to practice improvements.

Kim

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Collapse SubdiscussionKate Blue

Kate Blue

SaturdayJan 30 at 11:22am

Dr. Kyzar and class,

What is a normal distribution and what does it look like? Why is the normal distribution important in statistics?

Normal distribution is also called bell-shaped curve distribution. The sampling distribution presents a wave curve that is symmetrical. When sample sizes are large the data tends to result in a normal distribution. When normal distribution of the study sample is achieved, it will always be equal to the general population. Looking at the standard deviations of the data helps tell the accuracy of the sample. With a normal distribution pattern, sixty-eight percent of the data is included within one standard deviation to the left and right. Therefore, the accuracy of data in a normal distribution is high (Polit, 2016). A DNP scholar would put a higher preference on a study's data that resulted in normal distribution due to the accuracy of sampling reflecting the normal population.

Reference

Polit, D. F. (2016). Nursing research: Generating and assessing evidence for nursing practice (10th ed.). Wolters Kluwer Health.

Kate Blue

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Collapse SubdiscussionCarlos Legra Elias

Carlos Legra Elias

SaturdayJan 30 at 12:48pm

Hello Dr Kyzar and Class

Normal distribution can also be referred as a Gaussian distribution which is a distribution of possibility that happens to be symmetric in relation to the mean, which is an indication that any data found close to the mean tend have an occurrence that is more frequent in comparison to data that is not close to the mean. When it is illustrated in a graph, it assumes the shape of a bell. The distribution that is normal has various properties that are interesting which include; has equal median as well as mean, has a bell shape in addition to having a 68% of its data falling within the deviation of 1 standard (Jabbari Nooghabi, 2020).

The deviation that is standard is the one in that is in control of the distribution's spread. A standard deviation that is smaller is an indication that the data is clustered closely around the given mean, while normal distribution will end up being taller. Standard deviation that is taller shows that the spreading of the data is sparse near the mean hence the normal distribution tends to be wider and flatter. Has at the center is basically symmetric, 50% of the values tend to be at the left side of the center and 50% of the values are situated at the right. The general region under the cover basically is one and a normal model standard.

The importance of the normal distribution within statistics is mainly because of its capability of being in a position to fit many phenomena that are natural. For example, measurement error, heights, scores related to IQ in addition to blood pressure are done as per the distribution that is natural (Kim, et.al, 2020).

References

Jabbari Nooghabi, M. (2020). Process capability indices in normal distribution with the presence of outliers. Journal of Applied Statistics, 47(13-15), 2443-2478.

Kim, C., Cho, S., Sunwoo, M., Resende, P., Bradaï, B., & Jo, K. (2020). A Geodetic Normal Distribution Map for Long-term LiDAR Localization on Earth. IEEE Access.

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Collapse SubdiscussionCarlene Yearwood

Carlene Yearwood

SaturdayJan 30 at 4:31pm

Dr. Kyzar and class,

A normal distribution is a continuous probability distribution that is symmetrical on both sides of the mean, so the right side of the center is a mirror image of the left. The area under the normal distribution curve represents probability and the total area under the curve sums to one. Most of the continuous data values in a normal distribution tend to cluster around the mean, and the further a value is from the mean, the less likely it is to occur. For a perfect normal distribution the mean, median and mode are measures of central distribution of numerical values important for any research findings. The normal distribution is often called the bell curve because the graph of its probability density looks like a bell.

The normal distribution is the most important probability distribution in statistics because many continuous data in nature and psychology displays this bell - shaped curve when compiled and graphed for evidence. A normal distribution frequency curve can be used to measure continuous variables, such as IQ, height, weight and blood pressure. As a DNP scholar a normal distribution is an important factor to consider towards the contribution of accurate results for a practice change.

Reference

McLeod, S. A. (2019). Introduction to the normal distribution ( bell curve). Simply psychology: https://www.simplypsychology.org/normal-distribution.html

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Collapse SubdiscussionYosvani Garcia Boss

Yosvani Garcia Boss

SaturdayJan 30 at 9pm

Hello Dr. Kyzar,

Normal distribution which is also referred to as Gaussian distribution, is basically a distribution of probability considered to be symmetric in relation to the mean, which indicates that the data that is close to the mean tend to be more frequent within their occurrence as compared to the data that happens to be far as from the mean. When in a graph form, the normal distribution appears to be in the form of a bell curve. The distribution is said to be an appropriate term in relation to a bell curve of probability. Within a distribution that is normal, mean happens to be zero while the standard deviation ends up being one. This means its skew is zero while the kurtosis is three. These types of distributions happen to be symmetrical though it is not possible to say that every distribution that is symmetrical is normal (Martínez-Flórez, et.al, 2020).

Distributions considered to be normal tend to have a regular appearance in relation to statistics, in addition, they are known to have some properties that are interesting which include having the shape of a bell, has a median as well as a means that are equivalent in addition to a data falls of 68% within a standard deviation of 1. However, in reality, most distributions for pricing can not be said to be normal perfectly. The model of this distribution tends to be motivated by the theorem of Central limit. It is a thesis stating that the calculated averages from the variables that are independent as well as identically distributed randomly tend to have distributions that are approximately normal, despite of the form of distribution where the variables get to be sampled from as long as it has a variance that is finite (Mirfarah, et.al, 2021).

A times the normal distribution tends to be confused with the distribution that is symmetrical. The symmetrical distribution involves having the dividing line producing two images mirroring each other, however, the real data might be in form of humps that are two or a sequence of hills as well as the bell curve indicating a distribution that is normal.

The main reason as to why normal distribution is of great significance within statistics is due to the fact that it fits into many phenomena that are natural. For instance, blood pressure, heights, scores of IQ in addition to measurement error adhere to the distribution that is normal. The distribution that is normal is a function of probability used in describing the manner in which a variable value gets to be distributed. It is known as a distribution that is symmetric whereby most of the given observation tends to cluster all over the peak that is central in addition to the possibilities for values that are at a far distance from the taper off of the mean equally within the two directions. Values that are extreme within the two distribution tails tend to be similarly not likely (Lee and McLachlan, 2020)

The statistical tests that are most powerful by the name parametric which tend to be utilized by the psychologists need the data to be distributed normally. In case the data is not in resemblance with a curve in the bell shape, researchers might be forced into using a type that is considered to be less powerful in relation to the statistical test, which is referred to as statistics that are non-parametric.

References

Lee, S. X., & McLachlan, G. J. (2020). On mean and/or variance mixtures of normal distributions. arXiv preprint arXiv:2005.06883. Retrieved from https://arxiv.org/abs/2005.06883 (Links to an external site.)

Martínez-Flórez, G., Leiva, V., Gómez-Déniz, E., & Marchant, C. (2020). A family of skew-normal distributions for modeling proportions and rates with zeros/ones excess. Symmetry, 12(9), 1439. Retrieved from https://www.mdpi.com/2073-8994/12/9/1439 (Links to an external site.)

Mirfarah, E., Naderi, M., & Chen, D. G. (2021). Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions. Computational Statistics & Data Analysis, 107182. Retrieved from https://www.sciencedirect.com/science/article/pii/S0167947321000165 (Links to an external site.)

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Collapse SubdiscussionTheresa Kyzar

Theresa Kyzar

SundayJan 31 at 6:25pm

Hi Yosvani:

Thank you for your thoughtful response. Excellent! I really appreciated the insight you provided about the main reasons that the normal distribution is very significant in statistics and I strongly agree with these points.

Please allow me to add to your comments.

With a normal distribution, you should expect to observe approximately 68% of values within one standard deviation; about 95% of the values within two standard deviations; and about 99.7% are within three standard deviations. This is referred to as the 68 95 99.7 rule or Empirical Rule (Statistics How To, 2019). Exactly half the data is to the left as well as the right side of the mean. To visualize this, with x being the horizontal plane of the graph showing the data value scale and y being the vertical plane showing the frequency scale (Vetter, 2017). An example could be a group of individuals who are participating in a weight loss program. The x would be the weights with the distribution ranging from 150 lbs. to 350 lbs. The frequency would be how often each weight was recorded. In a normal distribution, 250 lbs. would be the mean and median with a bell shape. I think sometimes that students who are still novices with these kind of experiences struggle with how to set up their equations to properly understand the significance of the process involved with normal distribution. Your own thoughts about the importance of this and how non-parametric testing comes into play add meaning to this discussion.

Thank you and take care.

Kindly,

Dr. Kyzar

References

Statistics How To. (2019). What is the 68 95 99.7 rule? Retrieved from https://www.statisticshowto.datasciencecentral.com/68-95-99-7-rule/ (Links to an external site.)

Vetter, T. R. (2017). Fundamentals of research data variables: The devil is in the details. Anesthesia & Analgesia, 125(4), 1375-1380. http://dx.doi.org/10.1213/ANE0000000000002370 (Links to an external site.)

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Collapse SubdiscussionKimberly Austin

Kimberly Austin

SundayJan 31 at 12:19pm

What is a normal distribution and what does it look like? Why is the normal distribution important in statistics?

Normal distribution, which is also known as Gaussian distribution, or bell-shaped curve, is a symmetric, unimodal distribution, and not too peaked probability distribution (Polit & Beck, 2017).

Normal distribution is important in statistics as it is an essential tool used for analysis and interpretation of data (Kumar & Anila, 2017). Normal distribution fits many natural phenomena, such as height, weight, blood pressures, etc. This probability theory calculates corresponding values (Sokouti et al., 2017). As data is plotted, important findings are revealed which identify, standard deviation, mean, and mode.

References

Kumar, C. S., & Anila, G. V. (2017). On Some Aspects of a Generalized Asymmetric Normal Distribution. Statistica, 77(3), 161-79.

http://dx.doi.org.chamberlainuniversity.idm.oclc.org/10.6092/issn.1973-2201/7134 (Links to an external site.)

Polit, D. F., & Beck, C. T. (2017). Nursing research: Generating and assessing evidence for nursing practice (10th ed.). Wolters Kluwer Health.

Sokouti, M., Sadehhi, R., Pashazedeh, S., Eslami, S., Abgadi, H., Ghojazadeh, M., & Sokouti, B. (2017). Most accurate non-linear approximation of standard normal distribution integral based on artificial neural networks, Suranaree Journal of Science & Technology, 24(3), 263-280.

https://chamberlainuniversity.idm.oclc.org/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=127020973&site=eds-live&scope=site

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Collapse SubdiscussionTheresa Kyzar

Theresa Kyzar

SundayJan 31 at 6:17pm

Hi Angela, Kim, Carlos, Carlene, & Kate,

Thank you for your posts and for participating in this conversation. You have all provided excellent responses which expand upon the normal distribution!

Adding to your comments, I thought we could summarize the features of a normal distribution which include:

symmetric bell shape is noted;

the mean and median are equal; both located at the center of the distribution;

approximately equals, 68% of the data falls within one standard deviation of the mean;

approximately equals, 95%of the data fall s within two standard deviations of the mean; and

approximately equals, 99.7% of the data falls within three standard deviations of the mean.

normal distribution.svg

Take care,

Dr. Kyzar

References

Khan Academy. (2010, January 8). Normal distribution problems: Empirical rule [Video]. YouTube.

https://youtu.be/OhRr26AfFBU (Links to an external site.)

Khan, S. (2020). Normal distribution problems: Empirical rule. Retrieved from https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/stats-normal-distributions/v/ck12-org-normal-distribution-problems-empirical-rule (Links to an external site.)

Edited by Theresa Kyzar on Jan 31 at 6:18pm

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Collapse SubdiscussionRacheal Aneke

Racheal Aneke

SundayJan 31 at 9:24pm

What is a normal distribution?

The most important probability distribution in statistics (Links to an external site.) is normal distribution because it fits many natural occurrences and curves for a real-world random variable. It describes how the values of variables are distributed evenly. The normal distribution also functions for independent randomly generated variables. The readings are assembled at the top, and the probability values from the mean (Links to an external site.) are narrow or equal on both sides. Heights, weight, blood pressure, and IQ scores are examples of normal distribution (Gray. J., & Grove. S. K., 2021). Normal distribution is also called bell curve or the Gaussian distribution. The common thing about normal distribution is that mean, median (Links to an external site.), and mode (Links to an external site.) are all equal. The Empirical Rule or the 95% rule allows you to determine the proportion of values that fall within certain distances from the mean.

What does it look like?

Week 4 picture.png

This is a normal distribution with some interesting properties such as the bell shape or curve, the mean and median are equal, and 68% of the data are within a standard deviation (Gray. J., & Grove. S. K., 2021).

Why is the normal distribution important in statistics?

A hypothesis test assumes that figures follow a regular circulation in a normal distribution since the mean, median, and mode are equal. A normal distribution is essential in statistics because its probability distribution does not fit all populations to create variety. Linear and nonlinear degeneration (Links to an external site.) both assume that the residuals (Links to an external site.) also follow a normal distribution (Gray. J., & Grove. S. K., 2021). The central limit theorem (Links to an external site.) in a probability theory established that, in some situations, if independent variables are added, the sum normalizes the curve even if the original variables were not distributed normally.

Reference:

(Gray. J., & Grove. S. K., 2021) Burns and Grove's the practice of nursing research: appraisal, synthesis, and generation of evidence. Elsevier.

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Collapse SubdiscussionEjiro Ohonbamu

Ejiro Ohonbamu

SaturdayJan 30 at 6:18pm

Good evening Dr. Kyzar and classmates.

Appraising Descriptive Statistics

What statistical procedure is needed to determine an effective sample size to make a reasonable conclusion? Explain your rationale.

Quantitative research studies use a power analysis to approximate an actual sample size needed for a practical deduction. However, large sample sizes are desirable to small samples. The reason for this is that the large samples boost statistical conclusion legitimacy, which tends to be more typical. The researchers performed a power analysis at the early stage of the study to estimate the sample size and to assist in the reduction of possible errors of Type II (Polit & Beck, 2018). Basically, sample size defines the number of participants needed in a study. If the research calls for a specific sample to determine a specific outcome, it is essential that that is followed. On that note, with every large or small sample, there is a probability of errors if the sampling technique is not followed. The standard deviation promotes caring for the certainty that the sample is not typically dispersed.

The importance of the Chi-square value is noted by using the appropriate degree of freedom and significance (Turhan, 2020). Usually, the Chi-square determines the relationship between the two existing variables in a sample setting and the probability to show an actual relationship amongst the two variables in a given situation. It also assesses some uncompromising variables are connected with some populations, because variables tend to be a bit diverse from their populations (Turhan, 2020). In data analysis, it is mandatory to find degrees of freedom, expected occurrences, test statistics, and P-value connected to the test statistic (Turhan, 2020).

The researcher reports that the p-level led her to conclude that the null hypothesis was rejected. In your critique of the study, you determine that the null hypothesis is correct. Do these findings impact your decision about whether to use this evidence to inform practice change? Why or why not?

It is essential to note that the value P is the observation possibility of a sample statistic that is the highest test of statistics (Turhan, 2020). Now each hypothesis test uses the p-value to assess the depth of evidence. It shows that the null hypothesis untrue, which establishes that this could be a mistake. The null hypothesis is truthfully based on statistical errors and might institute further need added investigation. On that note, Type I error occurs when the null hypothesis is rejected when it is true. There is a greater risk of a Type I error with a 0.05 level of importance as compared to a 0.01 level of significance. The higher the level of significance, the more extreme, nature of the risk of a Type I error diminishes (Polit & Beck, 2017).

The null hypothesis is not obviously voiced in many research studies. In this case, it is, and it will impact my decision because an error has been determined by the researcher. In particular, scientists are challenged and not convinced with time‐to‐event results intensely understanding the null hypotheses based on hazard roles and their uses (Stensrud et al., 2019).

References

Polit, D. F., & Beck, C. T. (Eds.). (2017). Nursing research: Generating and assessing

evidence for nursing practice (10th ed.). Wolters Kluwer. 

Stensrud, M., J., Roysland, K., & Ryalen, P., C. (2019). On null hypotheses in survival analysis.

Biometrics. 75(4),1276-1287. http://doi:10.1111/biom.13102.

Turhan, S., N. (2020). Karl Pearson's Chi-Square Tests. Educational Research and Reviews,16

(9), 575-580. https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=EJ1267545

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Collapse SubdiscussionTheresa Kyzar

Theresa Kyzar

SundayJan 31 at 6:28pm

Hi Ejiro:

Good response this week! You offered some very interesting perspectives, and I would like to take this brief opportunity to add to your discussion. My comments relate specifically to the use of the Chi Square Analysis. This type of test along with correlations, t-tests, and ANOVA, are foundational techniques, typically covered in introductory statistics textbooks and introductory statistics classes. Chi-square tests are by far the most popular of the non-parametric or distribution free tests and the default choice when applied psychological researchers analyze categorical data (Sharpe, 2015). It is important to note that it is an important, useful when both variables are nominal-level data, e.g., simple counts of people within a category such as gender or ethnic group membership). Tappen (2016) discusses that the Chi-square test compares the observed (actual) frequencies in each cell to the expected frequencies (p. 350). However, remember that a key objection is that when the total number of observations is under thirty or when one or more expected cell frequencies are under five for total numbers under fifty then Fisher's exact test should be used in place of the Chi-square test (Langley, 1970; Siegel, 1956; Zar, 1974)[as cited by Hoffman, 1975]. Failure to do so may lead to an erroneous probability of rejecting the null hypothesis.

Thank you and take care.

Kindly,

Dr. Kyzar

References

Hoffman, J.E. (1975). The incorrect use of Chi-square analysis for paired data. Clinical and Experimental Immunology, 24, 227-229.

Sharpe, D. (2015). Chi-square test is statistically significant: Now what? Practical Assessment, Research, and Evaluation, 20(8). doi: https://doi.org/10.7275/tbfa-x148 (Links to an external site.). Retrieved https://scholarworks.umass.edu/pare/vol20/iss1/8 (Links to an external site.).

Tappen, R. (2016). Advanced nursing research: From theory to practice (2nd ed). Jones & Bartlett.

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Collapse SubdiscussionTheresa Kyzar

Theresa Kyzar

SundayJan 31 at 6:12pm

Important PLEASE READ: Week 4 Content Summary

Hi Class:

As we approach the weekend, here are tips from Week 4 and Week 5. These tips will assist you as you prepare for the week 5 quiz!

Week 4 Descriptive Statistics Key Points & Questions Properties of Descriptive Statistics (Polit & Beck, 2017)

Key Points-Descriptive Statistics

Summarize or describe characteristics of a data set.

They are numerical and graphical summaries of data.

Consist of two basic categories of measures: measures of central tendency and measures of variability or spread.

Measures of central tendency describe the center of a data set.

Measures of variability or spread describe the dispersion of data within the set.

Power Analyses (Ali & Bhaskar, 2016; Polit & Beck, 2017)

Help decide how large of a sample is needed to make sure judgments about statistical findings are accurate and reliable.

Prevent the recruitment of too many or too few numbers of subjects.

Must be used to determine sample size before the study begins.

Chi-Square Analysis (Ali & Bhaskar, 2016; Connelly, 2019; Polit & Beck, 2017)

Is a type of inferential statistic.

o Evaluates if two categorical variables (e.g., gender, educational level, race, etc.) are related (correlated) in any way.

o Appropriate for discrete variables (nominal, ordinal).

o Does not work with continuous variables (interval, ratio)

Null Hypothesis Testing (Ali & Bhaskar, 2016; Polit & Beck, 2017)

o The beginning point for statistical significance testing.

o A formal approach to deciding between two interpretations of a statistical relationship in a sample

o Null Hypothesis – suggests there is no relationship between variables, populations, etc. meaning there was an error in sampling.

o Alternative Hypothesis – suggests there is a relationship between variables, populations, etc.

o Rejecting the Null Hypothesis – suggests being in support of the Alternative Hypothesis.

Inferential Statistics (Ali & Bhaskar, 2016)

Allow one to make inferences (conclusions, predictions, associations, correlations) from data.

Take data from samples and make generalizations about a population.

Example: Say you are interested in an intervention to improve care at life’s end in the inpatient setting. Using inferential statistics, you take the data from your sample and assess whether or not the data can be expected to demonstrate that the intervention will work at the population level.

P-value (Taylor, 2019)

With most analyses, an alpha of 0.05 is used as the cutoff for statistical significance.

o If the p-value is less than 0.05, we reject the null hypothesis that there's no difference between the means and conclude that a significant difference does exist

o If the p-value is larger than 0.05, we cannot conclude that a significant difference exists.

o The p-value is also known as the calculated probability.

o The p-value is commonly referred to as the alpha.

Questions for your review as you prepare for the Week 5 Quiz.

What are inferential statistics used for?

Inferential statistics are used to make inferences (conclusions, predictions, associations, correlations) from a sample to a larger population (Ali & Bhaskar, 2016).

What is it called when research findings and conclusions from a study conducted on a sample population are used with the population at large?

Generalizability is the term used to describe when research findings and conclusions from a study conducted on a sample population are used with the population at large (Ali & Bhaskar, 206; Polit & Beck, 2017).

What are some examples of nominal and ordinal variables?

Interval – weight, height

Ratio – Level of pain: 0 to 10

Nominal – gender, blood type, marital status, hair color

Ordinal – socioeconomic status (e.g., low, middle, high), course grades (e.g., A, B, C), high school class ranking (e.g., 1st, 9th, 45th...)

What is a normal distribution and what does it look like?

Represents the distribution of many random variables as a symmetrical bell-shaped graph.

What are some of the properties of descriptive statistics?

Summarize or describe characteristics of a data set.

They are numerical and graphical summaries of data.

Consist of two basic categories of measures: measures of central tendency and measures of variability or spread.

Measures of central tendency describe the center of a data set.

Measures of variability or spread describe the dispersion of data within the set.

What is the most precise definition of a sample?

The sample is a subset of the larger population that a researcher aims to study.

What is the difference between the p-value and alpha?

When performing hypothesis testing in statistics, a p-value helps to decide the significance of results. A p-value is a number between 0 and 1.

A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so the null hypothesis is rejected (Taylor, 2019).

The alpha level is the probability of rejecting the null hypothesis when the null hypothesis is true or the probability of making a wrong decision (Taylor, 2019).

What is the name of the hypothesis that is accepted when significant differences exist?

Alternative hypothesis

What is random sampling and why is it important?

Random sampling is choosing small groups (subsets) of a population with each person having an equal chance of being chosen. Random sampling is important in that is supposed to be representative of the larger population (Polit & Beck, 2017).

Random sampling controls sampling bias also called sampling selection bias (Krautenbacher, Theis, & Fuchs, 2017).