Discussion Thread: Selecting and Interpreting Inferential Statistics
Respond to the following short answer questions from Chapter 5 of the Morgan, Leech, Gloeckner, & Barrett textbook:
D4.5.1 Compare and contrast a between-groups design and a within-subjects design.
D4.5.2. What information about variables, levels, and design should you keep in mind in order to choose an appropriate statistic?
D4.5.3. Provide an example of a study, including the variables, level of measurement, and hypotheses, for which a researcher could appropriately choose two different statistics to examine the relations between the same variables. Explain your answer.
D4.5.6. What statistic would you use if you wanted to see if there was a difference between three ethnic groups on math achievement? Why?
D4.5.8. What statistic would you use if you had one independent variable, geographic location (North, South, East, West), and one dependent variable (satisfaction with living environment, Yes or No)?
D4.5.9. What statistic would you use if you had three normally distributed (scale) independent variables (weight of participants, age of participants, and height of participants), plus one dichotomous independent variable (academic track) and one dependent variable (positive self-image), which is normally distributed?
Explain your answer.
In the thread for each short-answer discussion thestudent will post short answers to the prompted questions. The answers must demonstratecourse-related knowledge and support their assertions with scholarly citations in the latest APAformat. Minimum word count for all short answers cumulatively is 200 words.
or each thread thestudent must include a title block with your name, class title, date, and the discussion forumnumber; write the question number and the question title as a level one heading (e.g. D1.1Variables) and then provide your response; use Level Two headings for multi part questions (e.g.D1.1 & D1.1.a, D1.1.b, etc.), and include a reference section.
Reply:
The student must then post 1 reply to another student’s post. The reply must summarize thestudent’s findings and indicate areas of agreement, disagreement, and improvement. It must besupported with scholarly citations in the latest APA format and corresponding list of references.The minimum word count for Integrating Faith and Learning discussion reply is 250 words.
BUSI 820: Quantitative Research Methods
D3.4.1: Mean Visualization Score, Skewness & Mosaic Test Minimum
(a) Mean visualization test score is 5.24, indicating a slightly above-average performance (Morgan et al., 2020).(b) Skewness for math achievement is 0.044, effectively symmetrical and acceptable under the ±1 rule—thus suitable for parametric methods. Such mild skewness typically doesn’t compromise results (Iacobucci et al., 2025).(c) The mosaic test minimum is –4.0, which is possible when scoring penalizes wrong answers.
D3.4.2: Skewness > 1 and Boxplot Confirmation
(a) Only the Competence Scale has high skewness at –1.63—beyond ±1.0.(b) Such a distribution challenges normality assumptions and may necessitate transformations or nonparametric tests. However, mild skewness may not always critically bias results, though here it’s pronounced (Iacobucci et al., 2025).(c) The boxplot shows a longer lower whisker and median skewed upward, visually confirming the negative skewness (Morgan et al., 2020).
D3.4.3: Missing Data Overview
(a) There are 4 participants with missing data (75 total minus 71 valid).(b) Thus, 94.7% of students have valid motivation or competence scores. The TARMOS framework encourages explicit reporting and transparency in cases like this (Lee et al., 2020).(c) From the outputs alone, we cannot tell how many are missing both scores, which separate counts do not provide cross-variable overlap.
D3.4.4: Dichotomous Variables & Sample Details
(a) Means for binary variables represent proportions, for example, a mean of 0.55 on academic track indicates 55% in regular track and 45% in fast track (Morgan et al., 2020).(b) N = 75 participants total.(c) All 75 provided complete data for these dichotomous items.(d) 45% are on the fast track (100% – 55%).(e) 79% took Algebra 1 in high school, based on a mean of 0.79.
D3.4.5: Ethnic Proportions & Visualization Scores
(a) 9.6% of students identify as Asian-American.(b) 8% scored exactly 6 on Visual Test 2.(c) 66.7% scored 6 or less, as indicated by the cumulative percent.
References
Iacobucci, D., Román, S., & Moon, S. (2025). A tutorial on what to do with skewness, kurtosis, and outliers: New insights to help scholars conduct and defend their research. Psychology & Marketing
Lee, K. J., Tilling, K., Cornish, R. P., Little, R. J. A., Bell, M. L., Goetghebeur, E., Hogan, J. W., & Carpenter, J. R. (2020). Framework for the treatment and reporting of missing data in observational studies: The TARMOS framework. Links to an external site.
Morgan, G. A., Leech, N. L., Gloeckner, G. W., & Barrett, K. C. (2020). SPSS for introductory statistics: Use and interpretation (7th ed.). Routledge.
