BUSI820-Quantitative Research Methods (B05)

D7.9.1 (a) Under what conditions would you use a one-sample t-test?

The one-sample t-test can be used to compare the mean of a single group or sample to a hypothesized population mean or to compare the mean of a sample to that of a different study source (Morgan et al., 2020).

(b) Provide another possible example of its use from the HSB data.

The HSB data set, when compared with national norms, can be used in a collaborative manner with a series of various other tests such as the visualization test, the mosaic pattern test, and others. This collaborative approach ensures that all aspects of the data are considered, enhancing the accuracy of outcomes (Morgan et al., 2020).

D7.9.2 In Output 9.2: (a) Are the variances equal or significantly different for the three dependent variables?

The output provided in 9.2 does not show significantly different variances for the three dependent variables. Morgan mentions that the variances are not significantly different statistically, which means the assumption of equal variances is not violated (Morgan et al., 2020).

(b) List the appropriate t, df, and p (significance level) for each t test as you would in an article.

It seems that below list would be the results for the t-test:

Math Achievement

Males: t(df) p = .009

Females: t(df) p = .010

Visualization Scores

Males: t(df) p = .020

Females: t(df) p = .040

Grades in High School

 Males: t(df) p = .369

 Females: t(df) = p = .413

(c) Which t tests are statistically significant?

Morgan mentions that fast track students showed a statistically significantly different from the students that took the regular track on math achievement as, t(73) = 2.70, p = .009 (Morgan et al., 2020).

(d) Write sentences interpreting the academic track difference between the means of grades in high school and also visualization.

The difference between females and males based on their high school grades is insignificant, yet the difference in visualization scores is significant based on the interpretation of the data (Morgan et al., 2020).

(e) Interpret the 95% confidence interval for these two variables.

Morgan emphasizes the 95% confidence interval as a crucial measure, representing the difference between the size of the sample and the population mean. In this case, the interval falls between +12.29 and –31.22 points, with a zero value suggesting no significant difference (Morgan et al., 2020).

(f) Comment on the effect sizes.

Effect sizes are more than just statistical results (p-values). They are key to understanding and conducting research, as they help identify potential comparisons and analyze elements such as confidence intervals, variances, and effect sizes. As Morgan points out, an effect size measure may not be readily available in the output, but it can be computed from the z provided with the test statistic (Morgan et al., 2020).

D7.9.3 (a) Compare the results of Outputs 9.2 and 9.3.

When comparing the results of the two outputs, one will notice that the sets have different assumptions. Therefore, the significance levels, as well as the results, are very similar to the t-test, yet the significant difference was not much between males and females on grades in high school) (Morgan et al., 2020).

(b) When would you use the Mann–Whitney U test?

When comparing two groups, the Mann–Whitney U is a good method and preferable when using ordinal dependent variable data. In addition, the Mann–Whitney U can be used when there is a violation based on the assumption of equal group variances (Morgan et al., 2020).

D7.9.4 In Output 9.4: (a) What does the paired samples correlation for mother’s and father’s education mean?

In this output, we delve into the correlation between the mother's and father's education levels in two samples. This correlation, represented by the correlation coefficient (r), is a practical tool that can be calculated by analyzing each participant's data in the study. A positive correlation suggests that one parent's education level is higher than the other, while a negative correlation indicates the opposite. This understanding, as Morgan (2020) notes, has significant implications for understanding the dynamics of paired sample correlation, which measures the correlations between the two pairs that are scored.

(b) Interpret/explain the results for the t test.

When interpreting the results for the t-test, the information provided shows if a statistically significant difference between the two means is in place. In this case, the males and females were significantly different when looking at their math achievements and visualization scores. However, it does not seem to affect high school grades significantly. Morgan discusses the crucial role of inferential statistics in understanding how a t-test can help us see the likelihood of the apparent difference that could occur by chance (Morgan et al., 2020).

(c) Explain how the correlation and the t test differ in what information they provide.

Correlation of the samples measures both the strength and direction of their linear relationship of the two variables. This provides us with an idea of the consistency of how one variable changes with another. In contrast, a t-test plays a crucial role in statistical analysis by comparing the means of two groups to determine a statistically significant difference between them (Morgan et al., 2020).

(d) Describe the results if the r was .90 and the t was zero.

When interpreting an r score result of .90 and a t score of Zero, the clarity of these results is evident. An r score of .90 would indicate a positive linear relationship between the two groups' education levels. Regarding the t-value scoring at zero, this would indicate no significant difference between the two groups being compared. Morgan mentions that when there is a value of zero, no significant difference may occur (Morgan et al., 2020).

(e) What if r was zero and t was 5.0?

If r was zero and t was 5.0, this would show no linear relationship between the two groups' education levels. However, if the t-value of 5.0 occurs, this indicates evidence that a null hypothesis exists.

D7.9.5 (a) Compare the results of Output 9.4 with Output 9.5.

When comparing the results of the two outcomes, the paired t-test data sets give similar statistical significance results to the Wilcoxon based on the same variables (Morgan et al., 2020).

(b) When would you use the Wilcoxon test?

If the variables are not normally distributed, then the Wilcoxon test would be the preferred method to use (Morgan et al., 2020).

Reference

Morgan, G. A., Leech, N., Gloeckner, G., & Barrett, K. C. (2020). IBM SPSS for Introductory

Statistics (6th ed.). Routledge.