Answer

Purpose

The purpose of this assignment is to critically evaluate the sample size, statements for meaningfulness, and statements for statistical significance. Then based on the evaluation of the scenarios provided, to provide an explanation of the implications for social change. The assignment will use scenarios 1 and 3

Evaluation of the sample size.

A sample size defined as a subset of the population under study. Selection of the correct sample ensure collection of valid data and results increasing the sample size is a way of improving detection of differences. The correct sample size influences the statistical power which is the probability of rejecting a null hypothesis if it is false or simply stated, the degree to which detection of a difference by the researcher is possible. Low statistical power makes it hard to detect differences even when they actually occur in the population. As a result, every researcher must evaluate these three items whose influence on the statistical power is key. First is the alpha, then the effect size and the sample size.

The alpha which is the probability of type I error and the sample size are under the control of the researcher. Therefore, selection of an alpha value by the researcher should be done carefully to ensure that correct inference is made and no error is made. If the researcher is unsure of the likelihood of making an error, as is in the cases of exploratory research, a larger alpha such as 0.1 should be used. This should be strengthened by selection of a larger sample size.

In scenario 1 the samples consisted of 65 students in four face-to-face classes at a traditional state university and 69 students in four online classes offered at the same university which is not very huge although it fits the conventional sample size of greater than 30. The p-value selected was 0.6 which was slightly above the conventional threshold of 0.05. From the data provided in this scenario the power of test is 0.4 which was weak indicating a high unlikeliness of detecting any differences (Warner, 2012).

Evaluation of the statements for meaningfulness

Given that the research was exploratory in nature the generalization of the results to all students may not be possible. In addition, considering that exploratory research is about collecting data and finding out where it leads, use of p-value to reach an inference is not recommended.

Evaluate the statements for statistical significance

A closer analysis of the information provided in the scenario, the null hypothesis that there is no difference in satisfaction levels in quantitative reasoning course between traditional classroom and online environments was rejected because the test results t (132) =1.8 had a p=0.074 which is lower than the set p-value of 0.1 (Frankfort-Nachmias, & Leon-Guerrero, 2015; Wagner, 2016). This indicates that there is difference in satisfaction levels in quantitative reasoning course between traditional classroom and online environments. As noted earlier this can be associated with the sample size which is greater than the conventional but still smaller in such a study.

Explanation of the implications for social change.

The implications of this results are that on average, students in online quantitative reasoning classes have higher levels of satisfaction than those in traditional set up, the difference is significant. With the results being significant it is imperative that educators develop medium of delivering knowledge that works better in producing satisfaction to the target consumers, the students.

Scenario 3

Evaluation of the sample size.

In scenario 3 the samples consisted of 663 women and 650 men taken from a convenience sample of public, private, and non-profit organizations which is very huge. The current cultural competency levels of the participants were measured. The p-value selected was 0.1 which was slightly above the conventional threshold of 0.05. From the data provided in this scenario the power of test is 0.9 which was strong indicating a high likelihood of detecting any differences present between the two groups.

Evaluation of the statements for meaningfulness

From the information given, the research was exploratory in nature the generalization of the results to all people may not be possible. In addition, considering that exploratory research is about collecting data and finding out where it leads, and in this case measuring one’s competency level and then using a p-value to reach an inference. Although the p-value may show significance the results may not be meaningful in the real world (Warner, 2010).

Evaluate the statements for statistical significance

From the information provided in the scenario, the null hypothesis that there is no difference in cultural competency scores between male and female participants was rejected because the test results t (1311) =2.0 had a p<0.05 which is less than the set p-value of 0.1 and even the conventional one of 0.05 (Frankfort-Nachmias, & Leon-Guerrero, 2015; Wagner, 2016). This indicates that there is difference in cultural competency scores between male and female participants. As noted earlier this can be associated with the sample size which is greater than the conventional. Although statistical significance is found the difference in the mean competency scores between the women and the men was 0.3 (9.2-8.9).

Explanation of the implications for social change.

The implications of this results are that although on average, women have a higher cultural competency scores than men the difference is very minimal and its application in real life for social change may not be considerable. In addition, men are known to be more knowledgeable in cultural requirements than the women thus the results presented in this scenario is unexpected. Cultural competency may not have any significant impact in delivering social change as this competency must be transferred to others for it to make significant impact.