WK6Assgn_Beal_R (2) (1)

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1 T Test Analysis Roswell Beal PhD of Science in Public Policy and Administration, Walden University Quantitative Reasoning and Analysis Professor Olivia Yu January 7th, 2023

2 Scenario One In scenario one as an international development researcher, I set out to determine African Citizens perceptions about the current levels of democracy today. The working research hypothesis (H1) is that due to various recent reforms, there is an increased view of the level of democracy today in African Citizens and can be represented as H1 = 6. Since development experts want to see a value of 6 on a scale of 1-10, I used SPSS with a test value of 6 to estimate the effect size. In doing so, determining whether perceptions of the current levels of democracy are statistically different from the value of 6 is possible by using a one sample t test. It should be noted that there isn't a good research design, so comparing attitudes before and after the reforms is not possible. This scenario utilizes the 2015 Afrobarometer dataset which has a mean for the Q1 variable of Age is 37.17. To begin analyzing the t test, a random sample was taken from the population of 100 out of 1000 respondents to estimate the population mean (Frankfort-Nachmias et. al., 2020). The first table shows a sample mean of 5.04 and SD being 3.058. A significance level of 0.05

3 represents a 5% risk or margin of error where the interval is wrong (Frankfort-Nachmias et. al., 2020). The test value representing the hypothesized population mean of 6 compared to the sample mean of 5.04 shows a mean difference of -.956 which means that the sample mean is less than the desired expected mean of the study (Frankfort-Nachmias et. al., 2020). The negative t value of -2.982 indicates that the level of democracy today is less than the research hypothesis and results in the null hypothesis being rejected and the research hypothesis being accepted (Frankfort-Nachmias et. al., 2020). Additionally, the 2 tailed p value (.004) shows that this research is statistically significantly different because the p value is less than the alpha level (.05). The effect size is considered small because Cohen’s D point estimate is -.313. An implication for social change could include utilizing these findings in determining which reforms by politicians incur the most meaningful perception change of the level of democracy perceptions today in African citizens. As it stands now, the meaningfulness cannot be fully determined simply because there is a significant difference between the p value and alpha level (Frankfort-Nachmias et. al., 2020). Scenario Two Scenario two expounds on the work being done as a development researcher by way of looking at the statistical differences in current levels of democracy after social change movements in North Africa compared to South Africa. This research also uses the Afrobarometer date set where the mean of Q1 Age is 37.17. In order to determine this, an independent t test will be used with a random sample of 100 out of 1000 respondents. The independent t test will be used to compare the means of South and North African respondents of the categorical variable of current levels of democracy.

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4 The above graphic shows the independent sample t test. Within the sample of the population, 39 respondents represent South African Citizens and 8 respondents represent North African Citizens. This means that within a random sample with the sample size of 100 out of 1000 respondents, there were more South African respondents than there are North African respondents which alters the findings (Frankfort-Nachmias et. al., 2020). The mean of South African respondents is 5.44 with a SD of 2.972 and a mean of 5.63 for North African Citizens and SD of 3.335. The null hypothesis is that the variances are equal (Frankfort-Nachmias et. al., 2020). The p-value of the difference of means is .720 according to Levene's test for equality of variances which at a conventional alpha level of .05 means that it is insignificant and leads to a failure of rejecting the null hypothesis and must assume equal variances and not meaningful (Frankfort-Nachmias et. al., 2020). When evaluating the equal variances not assumed, the t value is -.149 with a mean difference of -.189 and the CI as located between -3.046 & 2.668 also leading to the not rejecting the null hypothesis. The effect size of Cohen's D is -.062 which is less than zero and represents a small or possibly nonexistent effect. The findings of such research rely on the sample size and while the difference between the two categories is large, there is

5 statistical significance that reflects the meaningfulness of the findings which is none. A social implication of the findings could be that on average, South African Citizens respond more to social reforms than North African Citizens based on the amount of responses in the sample size and that further social change initiatives could improve the responsiveness of North African Citizens to political opponents in an election. Scenario 3 The 3rd and final scenario is located in the High School Longitudinal Survey data set, which has a mean for X1SES is 1.5. In the scenario of an educational researcher is seeking to learn whether high school students' perceptions about the utility of mathematics changes in their freshmen year to their senior years of schooling. In order to analyze the difference between these two categories, the variables used are T1 Scale of Students Mathematics utility and T2 Scale of Students Mathematics utility with a sample size of 100 respondents out of 100 with a CI level of 95%. The type of test utilized for such research is a paired sample t test with a random sample.

6 In the above graphics, it can be observed that the mean for N=78 T1 Scale of students mathematics utility is .0445 with a SD of 1.00797. For the second variable of T2 Scale of students mathematics utility with N=78, the mean is .0662 with a SD of 1.01107. When comparing the means of these two variables, T2 represents senior students while T1 is for freshmen. There is a slight uptick in the mean for seniors compared to the freshman mean that on average, senior students perceive a higher utility of mathematics than freshman students (Frankfort-Nachmias et. al., 2020). This found that by looking at the mean difference of -.02167 with a SD of 1.07214 and the true difference can be seen when observing the CI at 95% being between -.26340 for lower and .22006 for upper bound. The t statistic is -.178 with a p-value of .859 and since this value is larger than the alpha level of .05, it must be assumed that the null hypothesis is true and it cannot be rejected (Frankfort-Nachmias et. al., 2020). This also means

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7 that the findings are not not statistically significant and are not meaningful to determine students' utility preference difference between seniors and freshmen. The effect size of Cohen’s D is -.020 which means the effect is small. An implication for the research findings would be that since there is no statistically significant change between freshman and senior utility in mathematics, the opinions of respondents are unwavering with more mathematics courses and more research into the matter can determine if changes to the courses can increase students utility in mathematics over time.

8 References Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.

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