discussion response

Week 04 Discussion 01: Selecting and Interpreting Inferential Statistics

Jediah Logiodice

Liberty University, School of Business

BUSI820: Quantitative Research Methods

June 13, 2026

Author Note

Jediah Logiodice

I have no known conflict of interest to disclose.

Correspondence concerning this article should be addressed to Jediah Logiodice.

Email: [email protected]

D4.5.1 Between and Within Designs

This week’s reading examines two types of study designs used to assess differences or associations using inferential statistics. Two types are introduced: between-groups and within-subjects designs. Section D4.5.1.a and D4.5.1.b define the relationship between the two study types.

D4.5.1.a Between-groups Design

The primary attribute of a between-groups design is that relationships are measured among groups that are independent of one another, whether segmented by different factors or levels (Morgan et al., 2020). So, for example, in our ChapterSixData.sav, a between-groups study might focus on differences in happiness scores between participants who indicated “Never” and those who indicated “Very Often” for the Angered from Things out of Your Control variable.

D4.5.1.b Within-subjects Design

The primary attribute of a within-subjects design is that comparisons measure relationships resulting from changes in independent variables from within the same case subjects or between matched pairs (Morgan et al., 2020). So, for example, in our ChapterSixData.sav, a within-subjects design might focus on differences in individual participant happiness before and after they received their essay scores.

D4.5.1.c Comparing Between-groups and Within-subjects Design

When choosing between-groups or within-subjects studies, it is important to note that this decision affects the study's size, time requirements, and complexity (Budiu, 2023). In addition, certain factors will dictate the type of study available; e.g., while age may only be available for a between-groups comparison in a single study, age could also be used for within-subject longitudinal studies (Budiu, 2023). Finally, as pointed out in Morgan et al. (2020), the between-groups and within-subject designs will dictate the type of inferential statistic that can be used: e.g., independent-samples t or one-way ANOVA for between-groups samples, and paired-samples t or repeated-measures ANOVA for within-subjects samples.

D4.5.2 Choosing an Appropriate Statistic

According to Morgan et al. (2020), the number of independent and dependent variables being analyzed, as well as the number of levels of the independent variable, and the type (i.e., nominal, ordinal, dichotomous, or scale) of both independent and dependent variables, all impact the choice of appropriate statistics. In addition, as previously discussed, the design type of between-groups and within-subjects also determines which statistic is valid.

D4.5.3 Example of Study

The following section provides an example study, the variables used, the level of measurement, and a proposed hypothesis and associated statistics examining the relationship between two variables, using the CollegeStudentData.sav from Week 03.

D4.5.3.a Hypotheses for Study

H0: There is no relationship between hours studied per week and students’ GPA.

Ha: There is a positive relationship between hours studied per week and GPA, such that students who study more tend to have a higher GPA.

D4.5.3.b Types and Variables for Study

This is an associational study using an independent variable (e.g., hours of study per week) as an IV-attribute predictor, and a scale variable as the dependent variable (e.g., current GPA). In addition, given the direction of Ha, a one-tailed directional test would also be appropriate.

D4.5.3.c Levels of Measurement for Study

Given that there are two variables with five or more ordered levels, and the skewness of hours of study per week is close, but does not go over the ±1 cutoff, e.g., normality is not markedly violated, the correct statistics, according to Morgan et al. (2020) is Pearson product moment correlation or the bivariate regression statistic. However, because hours of study per week has skewness = 0.950, and unequal magnitude between the measurements, I could also treat that variable as ordinal, which would suggest Spearman's rho as the statistic.

D4.5.6 Differential Statistics Between Three Groups

The appropriate statistic is a one-way ANOVA because this is a between-groups statistic, the IV has 3 (or more) levels (e.g., ethnic groups), and the DV (e.g., math achievement) is an approximately normal scale variable (Morgan et al., 2020).

D4.5.8 Statistics for Two-Variables

The statistic for a 4-level independent variable and a dichotomous dependent variable would be a Chi-Square statistic (Morgan et al., 2020). The difference between D4.5.6 and D4.5.8 is that the dependent variable is dichotomous, and therefore, we cannot use parametric tests against it.

D4.5.9 Complex Statistical Choice

According to Table 5.4 in IBM SPSS for Introductory Statistics (Morgan et al., 2020), four IVs, in which three are normally distributed scale variables (e.g., weight of participants, age of participants, and height of participants), and the fourth variable is dichotomous (e.g., academic track), used to predict a single normally distributed scale DV (e.g., positive self-image) would require a multiple regression statistic. The answer of a multiple regression statistic is representative of the outcome identified in Figure 5.1 (Morgan et al., 2020) from this week’s reading, where three or more variables first lead to a choice around complex statistics, while the one DV is a normally distributed scale variable with predictors that are a mix of both normal/scale and dichotomous.

References

Budiu, R. (2023). Between-subjects vs. within-subjects study design. Nielsen Norman Group. https://www.nngroup.com/articles/between-within-subjects/Links to an external site.

Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for introductory statistics: Use and interpretation (6th ed.). Routledge.