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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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