DNP-BIO 2

What are Hypotheses, and How are They Used in Statistics? The concept of hypotheses is central to most studies that collect quantitative data and statistics. Hypotheses are also essentially about prediction. The hypothesis is a proposed explanation for an observation that leads to a prediction(s) that, through our investigation and use of statistics, we will seek to either confirm or reject and, in so doing, test the validity of the hypothesis. How are Hypotheses Built? Hypothesis testing uses statistics to determine the probability that a given hypothesis has merit or not. Data can be interpreted by assuming a specific outcome and using statistical methods to accept or reject the assumption. The usual process of hypothesis testing consists of four steps. First, hypotheses must be developed. Hypotheses are generally built from a previous observation or experience. A null hypothesis is commonly used in research to determine whether there is a real relationship between two measured phenomena. It offers the ability to distinguish between results that are the result of random chance or if there is a legitimate statistical relationship. The alternative hypothesis refers to something being tested (two measured phenomena) against the null, and observations commonly show a real effect combined with a component of chance variation (Joseph, 2020). Experimental Approaches For example, in investigation (b), the authors split the patients into two groups and subject one group to treatment with Symphadiol (Scott & Mazhindu, 2014). The manipulated group is known as the experimental group or treatment group; the group not subject to the manipulation is known as the control group. Variables: Considering that a hypothesis is a prediction concerning two or more variables, it is important to consider the role of each of the variables when we apply a statistical test. One variable will be the dependent variable, and at least one will be the independent variable. The following example in the box is about a Symphadiol experiment ((Scott & Mazhindu, 2014, p. 40)  

In this example, the objective was to test the hypothesis that a daily dose of Symphadiol enhances weight loss in clinically obese individuals, compared with just a calorie-controlled diet. In the experiment described above, the independent variable is the treatment group (either Symphadiol treated or control) the patients are assigned to, while the dependent variable is the weight loss. Weight loss is the variable that will be measured. In the above experiment, we could analyze the types of errors: The researcher establishes an experimental hypothesis before performing an experiment or research study to test it. In a similar condition, we establish a statistical hypothesis when we try the experiment results to see if they could have occurred by chance. The most common form of statistical hypothesis found is the hypothesis of no difference, often called the null hypothesis and given the symbol Ho. The alternative hypothesis symbol is Ha. As the name implies, this is the opposite of the null hypothesis (Scott & Mazhindu, 2014). The comparison of the two models is deemed statistically significant if, according to a threshold probability—the significance level—the data would be unlikely to occur if the null hypothesis were true. A hypothesis test specifies which outcomes of a study may lead to a rejection of the null hypothesis at a pre-specified level of significance while using a pre-chosen measure of deviation from that hypothesis (the test statistic, or goodness-of-fit measure). The pre-

The experiment aims to test the hypothesis that daily doses of Symphadiol enhance weight loss in clinically obese individuals, compared with just using a calorie-controlled diet. It was decided to select men between the ages of 30 and 40 for the study. It was also decided to look at the impact of exercise in conjunction with Symphadiol. The intended population of this study is all healthy (other than their obesity) obese male individuals who are sufficiently motivated to lose weight to join a diet network. The individuals must not take any medication except that required for minor ailments. In total, 60 males were recruited between the ages of 30 and 40. Each participant was given a health check before the start of the study, their heights were recorded, and they received educational material and diet plans giving details of a calorie-restricted diet (2000 kcal), which they declared they would follow. All the men attended weekly diet networks where they received support and encouragement from their fellow dieters and the clinical trial specialist nurse. Those individuals following an exercise regime also attended a gym and completed the equivalent of 30 minutes of cycling (16 km) three times per week. The 60 participants were distributed randomly to four experimental groups: group 1: calorie-controlled diet and placebo; group 2: calorie-controlled diet and Symphadiol; group 3: exercise regime, calorie-controlled diet, and placebo;

chosen level of significance is the maximal allowed "false positive rate". One wants to control the risk of incorrectly rejecting a true null hypothesis. What are Type I and Type II Errors? The process of distinguishing between the null hypothesis and the alternative hypothesis is supported by considering two types of errors. Type I and type II errors are opposites. A Type I error occurs when a true null hypothesis is rejected. A Type II error occurs when a false null hypothesis is not rejected. Hypothesis tests based on statistical significance are another way of expressing confidence intervals. In that sense, every hypothesis test based on significance can be obtained via a confidence interval, and every confidence interval can be obtained via a hypothesis test based on significance.  What Can be Done to Reduce Type I Errors? The level of significance α of a hypothesis test is the same as the probability of a type 1 error. Therefore, by setting it lower, it reduces the probability of a type 1 error. "Setting it lower" means you need stronger evidence against the null hypothesis H0 (via a lower p-value) before we will reject the null. Therefore, if the null hypothesis is true, it will be less likely to reject it by chance. Reducing α to reduce the probability of a type 1 error is necessary when the consequences of making a type 1 error are severe (perhaps people will die or a lot of money will be needlessly spent) (Bill, 2017). If the α level is decreased, we decrease the probability of a Type I error and increase the probability of a Type II error. Conversely, as the α level is increased, we increase the probability of a Type I error and decrease the probability of a Type II error. Because the power of the test is inversely related to the probability of a Type II error (power increases as the probability of a Type II error decreases), it follows that the power can be increased by setting a higher alpha level for rejecting Ho (Lammer & Badia, 2016). Test Statistics The p-value is a statistical calculation that allows us, as researchers, to accept or reject a null hypothesis based on a predetermined significance level or alpha. A p-value less than alpha allows the researcher to reject the null hypothesis based on sampled evidence. By rejecting the null hypothesis where no difference exists, we can quantitatively state that a difference exists (Creswell & Creswell, 2017). Effect size, another quantitative measure, allows us to determine how well an intervention is working within a target population. Using an experimental design, the researcher would establish a control group and an experimental group where the experimental group would receive the intervention. At the conclusion of the intervention, a comparative analysis is performed between the control and experimental groups to determine the effect size. The larger the effect size the greater the strength of the association (Rosenthal, 2008).

The confidence interval establishes the degree of certainty that under similar conditions the probability that sample values will fall within the upper and lower bounds around the mean or population parameter. With all things being equal, multiple samples from the target population would produce similar results containing the true parameter (Creswell & Creswell, 2017). What is the Difference Between Statistical and Clinical Significance? In medical terms, clinical significance (also known as practical significance) is assigned to a result where a course of treatment has had genuine and quantifiable effects. Broadly speaking, statistical significance is assigned to a result when an event is found to be unlikely to have occurred by chance (Zbrog, 2020). Clinical significance has key applications in vaccine testing, pharmaceutical testing, and other forms of medical research where the magnitude and specific implications of a particular intervention need to be measured and quantified. But it also has use in non-medical settings, too, where it can provide a more rigorous critique of a data set. Statistical significance has broad applications wherever one is looking to learn whether something happened by chance, including market research with A/B testing and opinion research with surveys or polls. It can also be useful in the early stages of pharmaceutical testing to determine whether further research is warranted (Zbrog, 2020). Distributions and Probabilities One important concept in statistics is the idea that numbers can be distributed in certain ways. What we mean by distributed is the frequency of occurrence of particular numbers. For example, a data set of the number of sexual partners everyone has during a lifetime could contain just the values 4 or 3, or another number. However, it’s much more likely to be a mixture of different numbers from higher to lower. The mixture is very important, mainly because the way the numbers are mixed or distributed will determine the type of statistical test to use. The easiest way to see how data combinations are assembled is to plot them in a frequency histogram (Lohner, 2021) The frequency histogram is essentially a type of bar chart where the y-axis is the frequency of occurrence of a particular case. On the x-axis, we have a scale that is bounded by the values of the lowest and the highest of the cases. In between are placed the values of the scale using suitable intervals. A bar is drawn that fills the whole of each measured interval; the bars' sides are parallel, and the width of the bar is held constant (Lohner, 2021). We constructed the histogram using a web generator using the data given in the age frequency table.

 What are Probabilities? Chance is a word that has the same meaning as the word probability. When we say, ‘What is the chance of patient X catching malaria?’ we could also say, ‘What is the probability?’ We could also say, ‘What is the likelihood?’ These phrases all have the same meaning: we want to know whether something is likely to happen or not. Of these terms, probability is used more by statisticians. It is given the capital P symbol. P is normally described as values between zero (not possible) and 1 (certainty). The probability that you will die is 1; the probability that you will meet Florence Nightingale is 0. Probability tells you how likely it is that an event will occur (Lohner, 2021).

Frequency Table Class Count 49-54 3 55-60 4 61-66 3 67-72 7 73-78 3 The Histogram Mean 64.8 Standard Deviation (s) 8.16024 Skewness -0.25062 Kurtosis -0.87125 Lowest Score 49 Highest Score 77 Distribution Range 28 Total Number of Scores 20 Number of Distinct Scores

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Lowest Class Value 49 Highest Class Value 78 Number of Classes 5 Class Range 6

Probability allows us to quantify the likelihood an event will occur. You might be familiar with words we use to talk about probability, such as “certain,” “likely,” “unlikely,” “impossible,” and so on. You probably also know that the probability of an event happening spans from impossible, which means that this event will not occur under any circumstance, to certainty, which means that an event will happen without a doubt. These extreme probabilities are expressed in mathematics as 0 (impossible) and 1 (certain). This means a probability number is always a number between 0 to 1. Probability can also be written as a percentage, which is a number from 0 to 100 percent. The higher the probability number or percentage of an event, the more likely it is that the event will occur (NIST/SEMATECH, 2013). How are Probabilities Linked to Statistics and Frequency Distributions? Frequency distribution is related to the probability distribution. While a frequency distribution gives the exact frequency or the number of times a data point occurs, a probability distribution gives the probability of occurrence of the given data point. How Can Frequency Distributions be Used to Make Predictions? Frequency analysis is used to predict how often certain values of a variable phenomenon may occur and to assess the reliability of the prediction. A probability frequency distribution is a way to show how often an event will happen. It also shows what the probability of each event happening is. A frequency distribution table can be created by hand, or you can make a frequency distribution table in Excel. A relative frequency distribution consists of the relative frequencies, or proportions (percentages), of observations belonging to each category.  What Types of Distributions are There? A probability distribution specifies the relative likelihoods of all possible outcomes. There are two major classes of probability distributions: discrete random variable and continuous random variable that takes on an uncountably infinite number of possible values (Siderova, 2018). Example: The normal (or Gaussian) distribution has a bell-shaped density function and is used in the sciences to represent real-valued random variables that are assumed to be additively produced by many small effects. For example, the normal distribution is used to model people's height since the height can be assumed to be the result of many small genetic and environmental factors (Siderova, 2018). A binomial random variable is the sum of nindependent Bernoulli random variables with parameter p. It is frequently used to model the number of

successes in a specified number of identical binary experiments, such as the number of heads in five consecutive coin tosses (Siderova, 2018).   Example: Normal Distribution Bell-shaped Curve The normal distribution is symmetric. That is, it has one peak in the middle at the average value and points are as likely to occur on one side of the average value as on the other. An example of this would be the distribution of time from conception until birth for humans. This is why we say babies are born at nine months give or take two weeks. The two weeks represent two standard deviations above and below 266 days. Later we will learn about standard deviations and how, with normal population distribution, we can apply the 68-95-99.7% empirical rule. If the sample size is fairly large, many natural measures appear to have a normal distribution.   References Bartee, L., Shriner, W., & Creech, C. (2017). Presenting data – graphs and tables. Openoregon.pressbooks.pub; Open Oregon educational resources. https:// openoregon.pressbooks.pub/mhccmajorsbio/chapter/presenting-data/ Links to an external site. Birkett, A. (2017). How to avoid being deceived by data. CXL. https://cxl.com/ blog/avoid-being-deceived-by-data/ Links to an external site. Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed
 methods approaches (5th ed.). SAGE Publications, Inc. (US). Deriel, J. (2021). Quora - A place to share knowledge and better understand the world. Quora.com. https://www.quora.com/ Links to an external site. Duquia, R. P., Bastos, J. L., Bonamigo, R. R., González-Chica, D. A., & Martínez- Mesa, J. (2014). Presenting data in tables and charts. Anais brasileiros de dermatologia, 89(2), 280–285. https://doi.org/10.1590/abd1806-4841.20143388 Links to an external site. Infogram. (2019). How to Choose the right chart for your data. How to choose the right chart for your data. https://infogram.com/page/choose-the-right-chart- data-visualization Links to an external site. Kinney, W. (2017). How can type 1 and type 2 errors be minimized? |Socratic. Socratic.org. https://socratic.org/questions/how-can-type-1-and-type-2-errors- be-minimized Links to an external site.

Lammer, & Badia. (2016). Experimental design: Statistical analysis.https:// uca.edu/psychology/files/2013/08/Ch10-Experimental-Design_Statistical- Analysis-of-Data.pdf Links to an external site. Rosenthal, J. A. (2008). Qualitative descriptors of strength of association and effect size.  https://www.tandfonline.com/doi/pdf/10.1300/J079v21n04_02 Links to an external site. Scott, I., & Mazhindu, D. (2014). Statistics for healthcare professionals : an introduction. Sage. Wendy. (2021). How can statistics be misleading blog whatagraph. Whatagraph.com. https://whatagraph.com/blog/articles/misleading-statistics Links to an external site.