Week 5 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 2016 Laureate Education, Inc. Page 1 of 2 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 <.05, indicating that women are more culturally competent than are men. These results tell us that gender-specific interventions targeted toward men may assist in bolstering cultural competency. 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. 2016 Laureate Education, Inc. Page 2 of 2 Scenario #1 Sample Size According to (Mugenda & Mugenda, 1999), a sample size of 5% of the entire population is good enough for analysis. In this case the university population is unknown. However, it is logical to assume 132 represents 5% or more. Statements for meaningfulness Rather than saying that \"rapidly approaching significance\" we should say that the P-value of 0.06 is on the edge of significance. The first statement suggests that the P-value is decreasing and to make it sound worse, the word rapidly has been used. This is not statistically correct. Statistical significance \"Since the study was exploratory in nature, levels of significance were relaxed to the .10 level\". In exploratory research, we are only interested in providing details where little of is known about the phenomenon. It may use a variety of methods such as trial studies, interviews, group discussions, experiments or other tactics for the purpose of gaining information. Thus, Hypotheses statements are not used since the research is not descriptive. With absence of hypotheses statements, P-values are not necessary. P-values and there critical counterparts are used in descriptive and correlation forms of research. Therefore the statement above isn't statistically sound. \"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)\". This statement isn't just statistically incorrect, but also misleading. T-test would not be applicable here as we have two groups which are further subdivided into 4 subgroups each. Samples are to be taken from each sub group and an Analysis of Variance performed (ANOVA). By using t-test, the researchers committed a statistical error. Furthermore, traditional threshold of 0.05 is always recommended for use. Social change The Scenario exhibits great depth of evidence of how p-values are misunderstood and misinterpreted in general. With more emphasis on the subject matter, these errors can be avoided in future. Positive social changes will do a great deal in appreciating and understanding the subject matter. Scenario 2: Sample size: The sample size is very small, 3 samples of European American (n = 36), African American (n = 23) and Hispanic (n = 18) are taken. Statements for meaningfulness: With mean score of 16.4 and standard deviation of 4.6, European Americans were observed to have higher levels of education compared to African Americans with mean score of 15.5 and a standard deviation 6.8. Hispanics have got an average educational background (mean M = 13.3, and standard deviation, SD = 6.1) Statements for statistical significance: with F= 1.789 and p-value 0.05, that is p=.175, I accept ho at .175 level of significance and conclude that across the three races, there are no educational attainment differences. Implications for social change: clearly there is race biasness in the study. A higher number of European Americans were used. Also, the number used across the three races were very small. These can be solved by using approximately equal statistical data values and using a large data to accommodate any errors that are likely to occur. Scenario 3: Sample size: The sample size is very large, 2 samples of 663 women and 650 men are taken. Statements for meaningfulness: With mean score,M= 9.2 and standard deviation ,sd= 3.2, women were therefore observed to have higher levels of cultural competency as compared to men with mean score of 8.9 ad standard deviation 2.1. Statements for statistical significance: with t = 2.0, df = 1311 and p-value < 0.05, I reject ho at 5% level of significance and conclude that women are more culturally competent than are men. Implications for social change: clearly there is gender biasness in the study. Gender-specific interventions targeted toward men may assist in bolstering cultural competency. Scenario 4: Sample size: The sample size is very large, 432 employees were considered. Statements for meaningfulness: With r=.87, there is a strong positive linear relationship between level of income and job satisfaction. That is as the value of level of income increases the value of job satisfaction also increases. And vice-versa is also true. Statements for statistical significance: with p-value < 0.01, I reject ho at 1% level of significance and conclude that value of correlation coefficient is significant. That is I can say that there is a significant strong positive linear relationship between level of income and job satisfaction. Implications for social change: It is expected that the job satisfaction should also be there with low level of income. But according to the study it increases with the increase in level of income