# Scenario Case study

First, Very First, Most First:

Review **2** of the 4 possible scenarios. Do not review only 1 and do not review 3 or 4. Review **2** of the 4 scenarios. Here’s how:

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*Identify the scenario you are evaluating and name the population.* Estimate the size of that population. Example: the population of scenario 1 seems to be students at a State University so you could estimate the number of students at a typical State University. The University of South Florida up the road from me has about 40,000 students

*Identify the independent variable (IV) and the dependent variable (DV).* Sometimes this is stated by the researchers and sometimes you have to ferret it out. In scenario 2, the IV and DV are given as Race and Education, respectively.

*Write a null hypothesis*. If the null hypothesis is not provided in the scenario, write a null hypothesis based on the information that is provided in the scenario. Each scenario addresses differences in an interval or ratio DV among a Nominal or Ordinal IV made up of 2 or more groups. So write the null hypothesis this way:

There is no difference in Education based on Race among (state/name the population).

*Critically evaluate the sample size.* This is tricky because the scenarios do not provide us with the right information to calculate an appropriate sample size. And you want to avoid stating that a sample size ‘*seems’ *to be the right size (very amateurish). What to do?

Click on the sample size calculator in the Statistical Power Skill Builder (how to calculate sample size), enter .95 for the confidence level, your estimate of the population, .05 for the margin of error and see what pops up for the ideal sample size. Compare that number to the sample size in the scenario and critically evaluate the sample size in terms of making a Type I or Type II error. For example, if the sample size is smaller than the ideal sample size, does the probability of making a Type I error increase or decrease. Do the same drill with a Type II error.

*Critically evaluate the scenario for meaningfulness. *Follow the guidance I provided in the Announcement Week 5 Discussion: How To Critically Evaluate The Discussion Scenario. Note: we can often relate meaningfulness to social change. That is, if the research is meaningful then it may have implications for social change. Try evaluating meaningfulness and social change in the same paragraph. But first, define meaningfulness and define social change. Cite, cite, cite.

*Critically evaluate the statements for statistical significance. *Compare the researcher reported p-value for the hypothesis test they conducted (either a t-test or an ANOVA) to the confidence level (usually .05).

If the reported p-value is greater than .05, then the researcher should fail to reject the null hypothesis and state that there is no statistical significance.

If the reported p-value is less than .05, then the researcher should reject the null hypothesis and state that there is statistical significance.

I know this is counter-intuitive. Just do it.

Add this for grins, “There is no such decision as ‘rapidly approaching significance.’ This is statistics, not a hurricane watch.”

Select 1 response to the following multiple choice question: What scenario would you find to be the least fun?

A. Having a root canal performed by an experienced dentist.

B. Having 4 root canals performed by an unsupervised novice dentist.

C. Having 21 root canals performed by a trained Capuchin monkey.

D. Trying to statistically determine differences in patient post-root canal pain levels based on the dentist’s training.

Pick 2 of the following scenarios below:

1. Critically evaluate two scenarios below based upon the following points:

2. Critically evaluate the sample size.

3. Critically evaluate the statements for meaningfulness.

4. Critically evaluate the statements for statistical significance.

5. Based on your evaluation, provide an explanation of the implications for social change using cited sources.

Scenarios 1.

The p-value was slightly above conventional threshold, but was described as “rapidly approaching significance” (i.e., p =.06).

An independent samples t test was used to determine whether student satisfaction levels in a quantitative reasoning course differed between the traditional classroom and on-line environments. The samples consisted of students in four face-to-face classes at a traditional state university (n = 65) and four online classes offered at the same university (n = 69). Students reported their level of satisfaction on a fivepoint scale, with higher values indicating higher levels of satisfaction. Since the study was exploratory in nature, levels of significance were relaxed to the .10 level. The test was significant t(132) = 1.8, p = .074, wherein students in the face-to-face class reported lower levels of satisfaction (M = 3.39, SD = 1.8) than did those in the online sections (M = 3.89, SD = 1.4). We therefore conclude that on average, students in online quantitative reasoning classes have higher levels of satisfaction. The results of this study are significant because they provide educators with evidence of what medium works better in producing quantitatively knowledgeable practitioners.

2. A results report that does not find any effect and also has small sample size (possibly no effect detected due to lack of power).

A one-way analysis of variance was used to test whether a relationship exists between educational attainment and race. The dependent variable of education was measured as number of years of education completed. The race factor had three attributes of European American (n = 36), African American (n = 23) and Hispanic (n = 18). Descriptive statistics indicate that on average, European Americans have higher levels of education (M = 16.4, SD = 4.6), with African Americans slightly trailing (M = 15.5, SD = 6.8) and Hispanics having on average lower levels of educational attainment (M = 13.3, SD = 6.1). The ANOVA was not significant F (2,74) = 1.789, p = .175, indicating there are no differences in educational attainment across these three races in the population. The results of this study are significant because they shed light on the current social conversation about inequality.

3. Statistical significance is found in a study, but the effect in reality is very small (i.e., there was a very minor difference in attitude between men and women). Were the results meaningful?

An independent samples t test was conducted to determine whether differences exist between men and women on cultural competency scores. The samples consisted of 663 women and 650 men taken from a convenience sample of public, private, and non-profit organizations. Each participant was administered an instrument that measured his or her current levels of cultural competency. The cultural competency score ranges from 0 to 10, with higher scores indicating higher levels of cultural competency. The descriptive statistics indicate women have higher levels of cultural competency (M = 9.2, SD = 3.2) than men (M = 8.9, SD = 2.1). The results were significant t (1311) = 2.0, p < .01, showing that as level of income increases, job satisfaction increases as well.

4. A study has results that seem fine, but there is no clear association to social change. What is missing?

A correlation test was conducted to determine whether a relationship exists between level of income and job satisfaction. The sample consisted of 432 employees equally represented across public, private, and non-profit sectors. The results of the test demonstrate a strong positive correlation between the two variables, r =.87, p < .01, showing that as level of income increases, job satisfaction increases as well.

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