1-3 page inferential statistic paper

When you are working on the Inferential Statistics Paper I want you to format your paper with the following information

I.                    Introduction – What are inferential statistics and what is the research problem and hypothesis of the article?

II.                  Methods – Who are the subjects and variables within the article?

III.                Results – What is the statistical analysis used, why were these tests chosen? What were the results of these tests and what do they mean?

IV.                Discussion – What were the strengths of this article? What would you have done differently in terms of variables and statistical analysis? Why?

V.                  Conclusion – Reiterate the introduction and include relevant information that answers the questions regarding the hypothesis.

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  Read:  Chapter 3 and 4 of Statistics for the Behavioral and Social Sciences.

         Participate in One discussion.

         Discussion 1 –Standard Normal Distribution– This allows you to look at any data set into the standard distribution form.

         Quiz – Hypothesis testing

         Submit your Inferential Statics Article Critique – Read Differential Effects of a Body Image Exposure Session on Smoking Urge Between Physically Active and Sedentary Female Smokers.  What is the research question and hypothesis? Identify what variables were present, what inferential statistics were used and why, and if proper research methods were used. See grading rubric for full details.

Discussion Post Expectations:

Your initial post (your answer) is due by Day 3 (Thursday) of this week for Discussion 1.

When grading the Standard Normative Distribution discussion I will be looking for your answer to contain:

Week 2 Discussion 1 Board Rubric
	Earned	Weight
Content Criteria		0.5
Student identifies and defines what Standard Normative Distribution (SND) is.
Student explains why it is needed to use a SND to compare two data sets.		0.5
Student identifies the purpose of a z-score in a SND.		0.5
Student identifies the purpose of a percentage in a SND.		0.25
Student explains whether a z-score or a percentage does a better job of identifying proportion of a SND.		0.25
The student responds to at least two classmates’ initial posts by Day 7.		1
Student uses correct spelling, grammar and sentence structure.		2
		5

 

Grading - The discussions are both worth a total of 5 points. The breakdown of the grading for this week’s assignment (per discussion assignment) will be as follows:

         Posting your answer by the due date (Day 3, Thursday) is worth 4 points. These five points will be based on the information outlined within the Discussion Assignment Expectations. Content will be worth 2 points and format; spelling and grammar will be worth 2 points.

         Responding to two of your classmates (for each assignment) is worth 1 point. The answers must be substantive and go beyond “I agree” or “Good job” to qualify for this point.

Intellectual Elaboration:

In Week 1 we looked at descriptive statistics and how we can use numbers and charts to explain how data looks and what it means.  This week we will look at inferential statistics which means we are looking at what the data means, or could mean, in practical application to a population (if we can prove or disprove a hypothesis) (Tanner, 2011).

 The z-test outlined in chapter 4 tells how we apply the z-score to the z-test.  One of the limitations of the z-test is that it does not allow us to compare two variables within two samples it only allows us to look at a sample group and applying it to a whole population.  In Week 1’s guidance we looked at a group of students test scores in a class.  With a z-test we can look at this sample and apply the results to all students who take the same course and make a prediction about how all students within the course will do on the same test.  What we could not do would be to look at the results of the test scores after preforming the z-test and compare it to the GPA’s of students within the class to see if students who received lower scores on the test also had lower GPA’s. Also without access to the mean of the population and the standard error of mean of the population all of the student’s GPA’s could not be determined, thus access to the data could also be a large hurdle to overcome to make this correlation (Tanner, 2011).

 Looking at the t-test, unlike a z-test which looks at a sample and applies it to a population the t-test allows us to look at the means of the two different groups being studied to see if they are statistically different from each other. The way this is most commonly used is within research to see if the independent variable had an effect on the population being studied and if a change in the population was made (ChangingMinds.org, 2012).   How does a t-test determine if the independent variable applied to a population caused change?  To do this researchers look at whether the null hypothesis is true, meaning that no change occurred. Researchers will look to see if the mean of the experimental sample is the same as the mean of the sample the experimental population is being compared to is the same. If it is then no change has occurred and the null hypothesis is true (Tanner, 2011).

So let’s say we have gathered the data and ran the t-test, how do we know what the results mean? Are the results significant (meaning that our alternative hypothesis is proved to be true)?  In order to do this we need 4 things.

1. The number of subjects we have. (df which is n – 1 or your total number of subjects -1)

2. To know if you have a one tailed or two tailed t-test (which we will look at more closely in Week 3).

3. The probability that you have chosen (typically .05).

4. T distribution critical values table (Gerstman, 2007). You can see this table below under the Additional Resources section.

When you use the df and look at the probability for the one or two tailed t-test you will see the what result you need from your t-test to see if your results are statistically significant. For example of you had a df of 15 (which means you had 16 subjects) and a p< 0.05 and a one tailed t-test you need a result at or above 1.753 in order for the results to be statistically significant, meaning there is a difference between the two variables you are testing and you would reject the null hypothesis and accept the alternative hypothesis.

For example if researchers were testing an HIV drug and wanted to see of Drug X had an effect of raising the white blood cell count they would test the group that received the independent variable (Drug X) against a control group that did not receive the drug. If after running the t-test they found that the group that received Drug X had a mean that was the same as the control group for the number of white blood cell’s present then there would be no change and they would accept the null hypothesis. In the event that the means of the population who received Drug X is different than the population that did not this would not mean that the drug works, it would mean they failed to reject the null hypothesis (Tanner, 2011) and that further study is needed to determine if Drug X has a therapeutic effect.

Charts from Week 1 provide visual representations of data.  What happens if we chart the data and it is hard to understand?  This is where the standard normal distribution comes into play. By applying this we can place data is the bell curve you are familiar with seeing. The tallest part of the bell curve will be the median of the scores. In this deviation all the data will be towards the center with no bias towards the right or the left when graphed out.  Some key factors about a standard normal distribution that may not be present in other forms of data is that there is a mean, median and mode which will be within the center of the data, approximately 50% of the data will be above the mean and 50% of the data will be below the mean, 68% of all the data will be within 1 standard deviation of the mean (1 deviation above and below the mean), 95% of the data will be within 2 standard deviations of the mean (2 deviations above and below the mean), and 99.7% of the data will be within 3 standard deviations of the mean (3 deviations above and below the mean (MathisFun, 2012).

(Pullen, 2010).

So knowing this, the question is why standardize your data, why not just graph it out and let it fall where it will?  The simplest answer it is that will make your job easier as you will only need one table and it will provide more accurate data to assist you with making your decision. If you look at the example of the grades there are several different tables to look at the grades to get the information you need.  What if you are teaching a class and you have 40 assignments and you were trying to find the same information? You would need to alter the data to get an idea of how many students fell in the A,B, C, D, and E range, a different graph to see if there was a skew in the data, if there is kurtosis etc. This type of graphing of data will also allow you to see probability, what is the likely-hood that a student will fall into each grade range (Tanner, 2011)?

Consider the following sample of students who took a test: 85, 90, 96, 77, 63, 86, 88, 72, 74, 98, 100, 85, 83, 72, 62, 87, 92, 93, 84, 86, 75, 82, 78, 73, 64, 74, 92, 87, 39, 55, 94, 79, 73, 88, 83, 84, 75, 67, 74, 86, 85, 67

You could do several calculations and find out the mean, median, mode and then determine how the class was doing by creating several different graphs using several different calculations. Or you can use the standard normal distribution to analyze all the data at once.

Tests
Mean	79.69048
Standard Error	1.882584
Median	83
Mode	85
Standard Deviation	12.20054
Sample Variance	148.8531
Kurtosis	1.767116
Skewness	-0.99429
Range	61
Minimum	39
Maximum	100
Sum	3347
Count	42

 

What the analysis tells us is that the Mean Score (0 of the Standard Normative Deviation) is 79.69 and the standard deviation is 12.20 points. So 68% of the data will fall between 67.49 (which is -1 of the standard deviation) and 91.89 (which is +1 of the standard deviation). The skew of this data set is -.99 which means that there is a slight negative skew (more students fell above the mean than below the mean and that the median score is higher than the mean score).  Looking at the kurtosis of this data is 1.77. Looking we see that the standard deviation (s) is greater than R(  ) where R=Range of 61 divided by 6 so s>R/6 looks like 12.20>61/6 or 12.20>10.67.  This means that the kirtosis of this data set is platykurtic, meaning that the data within the set is too varied to be a normal curve and it is flatter as in figure 2.6 of your text (Tanner, 2011).

Additional Resources (web links, videos, and articles):

Independent Samples T-Test

http://www.youtube.com/watch?v=Ojo-n-riYj8

Statistics – Standard Normal Deviation

http://www.youtube.com/user/EducatorVids2?v=drk8yzFoWSE&feature=pyv

T Distribution Critical Values Table

http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf

Please watch video: Probability Distributions

 

 

References:

Gerstman, B. (2007). T Distrabution and Critcal Values Table. Retrieved from http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf

MathisFun (2012). Normal Distribution. Retrieved from http://www.mathsisfun.com/data/standard-normal-distribution.html

Pullen, P.C. (2010). Understanding Standard Scores. Retrieved from  http://www.faculty.virginia.edu/PullenLab/WJIIIDRBModule/WJIIIDRBModule7.html

Tanner, D. (2011). Statistics for the behavioral & social sciences. San Diego, CA: Bridgepoint Education, Inc.

Standard Normal Distribution

For this discussion, identify the appropriate application of standardized scores to reflect on their benefits and to interpret how test scores and measures are commonly presented.

Review Chapter 3 of your course text, which introduces probability and the standard normal distribution.  Examine the assumptions and limitations presented in these topics and then consider and discuss the following questions: 

· When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution?  

· What role do z-scores play in this transformation of data from multiple distributions to the standard normal distribution?  

· What is the relationship between z-scores and percentages?  

· In your opinion, does one do a better job of representing the proportion of the area under the standard curve?  Give an example that illustrates your answer.     

Guided Response:  Review your classmates’ posts.  Respond substantively to at least three peers.  What did you find useful about their explanations and examples?  What suggestions would you make for improvement?  Ask a question for further clarification as to the meaning and use of the z-scores.

Inferential Statistics Article Critique

Read the article "Differential Effects of a Body Image Exposure Session on Smoking Urge Between Physically Active and Sedentary Female Smokers," and identify the research questions and/or hypotheses as they are stated. Consider the following questions: What are the variables (sample sizes, population, treatments, etc.)?  What are the inferential statistics used in this article?  Were the proper steps of hypothesis testing followed?

Write a two- to three-page paper presenting the information listed below. Include a title page and reference page in APA style.  Cite any references made to the article within the body of the paper in APA style. Your paper should begin with an introductory paragraph (including a thesis statement) and end with a concluding paragraph summarizing the major points made in the body of the paper and reaffirming the thesis.  When writing the article critique, your paper must:

1. Determine what question(s) the authors are trying to answer by doing this research.

2. Determine the hypothesis being tested and the concepts that were applied in this process.

3. Evaluate the article and critique the statistical analysis employed in the study.

· Would you have included more and/or different variables? Explain your answer.

4. Examine the assumptions and limitations of the statistical study.

· What would you have done differently in this case? Why?

5. Identify how the authors applied statistical testing to the problem.

6. Interpret the findings of the author(s) using statistical concepts.

You may access the Critical Thinking Community website for tips on how to formulate your thoughts and discussion of these questions in a logical and meaningful manner. Writing the Article Critique The Assignment:

1. Must be two to three double-spaced pages in length (excluding title and reference pages), and formatted according to APA style as outlined in the Ashford Writing Center.

2. Must include a title page with the following:

a. Title of paper

b. Student’s name

c. Course name and number

d. Instructor’s name

e. Date submitted

3. Must document all sources in APA style, as outlined in the Ashford Writing Center.

4. Must include a separate reference page, formatted according to APA style as outlined in the Ashford Writing Center.