BUSI 820 Week 7 Discussion

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WEEK 7 DISCUSSION 1 D7.9.1(a) Under What Conditions Would You Use a One-Sample T Test? (b) Provide Another Possible Example of Its Use from the Hsb Data. D7.9.1(a) Under What Conditions Would You Use a One-Sample T Test? It is not unusual to seek a comparison between the average of a variable in your dataset and a different mean where individual scores are not available. One instance of this is evaluating a sample against the national standard. Additionally, you may wish to assess how the mean of your sample compares to that of a distinct study. For instance, if you're replicating a study on GPA, you might inquire how the GPA in your current study compares to the GPA observed in the replicated study of ten years ago. In another example, Muhammed Al-Kassab (2022) uses one sample t test to determine if the sample data is representative of the same population. D7.9.1(b) Provide Another Possible Example of Its Use from the HSB Data. We can contrast the mean values in the HSB dataset with the national standards for the mosaic pattern test, the visualization test, or the math achievement test. This comparison can serve to either substantiate that the HSB dataset aligns with the performance of all students or indicate a notable distinction between our HSB data and the national norms. D7.9.2 In Output 9.2 D7.9.2(a) Are the Variances Equal or Significantly Different for The Three Dependent Variables? The variances equal for math achievement test and grades in high school (the significant values of the F test are 0.466 and 0.451, higher than 0.05). The variances are significantly different for visualization test (the significant value of the F test is 0.013, less than 0.05). D7.9.2(b) List the Appropriate t, df, and p (Significance Level) for Each t Test as You Would in an Article.

WEEK 7 DISCUSSION 2 For math achievement test , t = 2.697, df = 73, and p = 0.009. For grades in high school , t = -0.903, df = 73, and p = 0.369/ For visualization test , t = 2.385, df = 57.150, and p = 0.020. D7.9.2(c) Which t Tests Are Statistically Significant? The t Test for visualization test is statistically significant. The t Test for math achievement test is statistically significant. The t test for grades in high school is not statistically significant. D7.9.2(d) Write Sentences Interpreting the Academic Track Difference Between the Means of Grades in High School and Also Visualization. The t Test for visualization test is statistically significant. Therefore, based on examining the means, we can conclude that fast tract students have higher visualization scores than regular track students. The t Test for math achievement test is statistically significant. Therefore, based on examining the means, we can conclude that fast tract students have higher math achievement test scores than regular track students. The t test for grades in high school is not statistically significant. Therefore, we can conclude that there is not enough evidence to say that there is a systematic difference between students in the fast track and students in the regular track on grades in high school . D7.9.2(e) Interpret the 95% Confidence Interval for These Two Variables. For math achievement test , the 95% confidence interval is between 1.04648 points and 6.96760 points. This means if we constructed an infinite number of studies using the same conditions, and computed a 95% confident interval of each study, 95% of the intervals would contain the true population difference between means.

WEEK 7 DISCUSSION 3 For visualization test , the 95% confidence interval is between 0.34761 points and 3.98094 points. This means if we constructed an infinite number of studies using the same conditions, and computed a 95% confident interval of each study, 95% of the intervals would contain the true population difference between means. D7.9.2(f) Comment on the Effect Sizes For math achievement test , d = 0.60. According to Cohen’s size effect table, the effect size is a medium or large. For grades in high school , d = 0.21. According to Cohen’s size effect table, the effect size is a small or medium. For visualization test , d = 0.60. According to Cohen’s size effect table, the effect size is a medium or large. D7.9.3(a) Compare the Results of Outputs 9.2 and 9.3. (b) When Would You Use the Mann–Whitney U test? D7.9.3(a) Compare the Results of Outputs 9.2 and 9.3. Note that, although the two tests are based on different assumptions, the significance levels (i.e., p values) and results were similar for the t test and the MW that used the same variables. The mean ranks of the academic track differ significantly on visualization test and math achievement test but not on grades in high school . D7.9.3(b) When Would You Use the Mann–Whitney U test? The Mann-Whitney U is used to compare two groups, as is a t test, but it should be used when we have ordinal (not normally distributed) dependent variable data. The M-W can also be used when the assumption of equal group variances is violated. D7.9.4 In Output 9.4:

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WEEK 7 DISCUSSION 4 D7.9.4(a) What Does the Paired Samples Correlation for Mother’s and Father’s Education Mean? The Paired Samples Correlation for Mother’s and Father’s Education is the correlation between the two paired scores. The correlation (0.681) indicates that highly educated men tend to marry highly educated women and vice versa. D7.9.4(b) Interpret/Explain the Results for the t Test. The significant level, p, was 0.019. Therefore, the difference in educational level is statistically significant, and we can tell from the means, that fathers have more education. We can tell from the confident interval that the difference in the means could be as small as 0.099 or as large as 1.079 on the 2 to 10 scale. D7.9.4(c) Explain How the Correlation and the t Test Differ in What Information They Provide. The correlation (0.681) means there is an association between the fathers’ education and mothers ‘education. On the other hand, the t-Test shows that there is a statistically significant difference between fathers’ education and mothers’ education. D7.9.4(d) Describe the Results If the r Was .90 and the t Was Zero. In this case, there is a strong association between fathers’ education and mothers’ education and there is not statistically significant difference in fathers' education and mothers' education. The two variables are highly correlated. D7.9.4(e) What If r Was zero and t Was 5.0? In this case, there is no correlation between fathers’ education and mothers' education. There is a significant difference in fathers' education and mothers' education.

WEEK 7 DISCUSSION 5 D7.9.5 (a) Compare the Results of Output 9.4 with Output 9.5. (b) When Would You Use the Wilcoxon Test? D7.9.5(a) Compare the Results of Output 9.4 with Output 9.5. The paired t test for father's and mother's education gives similar statistical significance results (p = 0.019) to the Wilcoxon (p = 0.037) for the same variables. D7.9.5(b) When Would You Use the Wilcoxon Test? The Wilcoxon test would be used when the variables are not normally distributed.

WEEK 7 DISCUSSION 6 References Morgan, G. A.; Barrett, K. C.; Leech, N. L.; Gloeckner, G. W. (2020) IBM SPSS for introductory statistics: Use and interpretation, sixth edition . Taylor and Francis. Kindle Edition. Muhammed Al-Kassab, M. (2022). The use of one sample t-test in the real data. Journal of Advances in Mathematics , 21. https://rajpub.com/index.php/jam/article/view/9279

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BUSI 820 Week 7 Discussion

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