Discussion Replies: Selecting and Interpreting Inferential Statistics

Rex S

Discussion Thread 4: Selecting and interpreting inferential statistics

Discussion Thread: 4

D4.5.1 Compare and contrast a between-groups design and a within-subjects design.

Morgan, Leech, Gloeckner, & Barrett (2020) note that much research places emphasis on variances between two or more groups (p. 86).  Social sciences in particular often seek to compare and contrast groups, peoples, categories, nations, philosophies, and cultures.  Grouping variables or categorical independent variables assign specific tendencies or traits to the variable then measure against it. 

Between groups establishes opportunity for both between-group studies, where each group remains separate from the other groups.  Within-group studies combines the study group into a single set aligned by one or more similar traits.  Additional presented models include: single-factor designs, between-groups factorial models, and mixed factorial designs.

 

D4.5.2. What information about variables, levels, and design should you keep in mind in order to choose an appropriate statistic?

Morgan et al (p. 88) suggest eight steps for statistic selection.  First, how many total variables exist in the hypothesis.  Too many and/or undefined variables can quickly fail a hypothesis.  Else, cause significant bias at the outset. 

Bivariate statistics follow.  Bivariate indicates differentiation from basic statistics.  Bivariate defines as a single independent and single dependent variable (p. 88).  If more than two then it becomes either complex or multivariate depending on context.  Third establish if variables are nominal or not.  Fourth, identify how dependent variables.  Finally, follow the path of dependent variables.  Single DV (e.g. dependent variable) follow one path.  While multiple related variables follow another. 

 

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.

Hypothesis: Worker turnover decreases with higher pay rates.

IV: Box plot payscale of 100 blue collar workers.

DV: The higher the payscale the lower the turnover rates.

An ANOVA (MANOVA) scale could be used to compare the two dependent variables.  “ANOVA has many variations including analysis of covariance (ANCOVA)” (Rosenstein, 2019, p. 52).  In this case, adding multiple dependent variables into a single analysis. 

 

Explain your answer.

 ANOVA, or Analysis of Variance, permits two variables to intersect and scale for example if high pay and low turnover intersect one could infer that the two positively correlate.  Similarly if low pay and high turnover remain segregate then one could infer the two negatively correlate or demonstrate inverse correlation.

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?

I would recommend a paired or matching statistic.  This works best both within subject designs and single-factor models. 

Why?

Paired and matching statistics provide comparisons where there are easy visualizations.  The math achievement score is a dependent variable while the three ethnic groups are independent variables.  A nominal scale names variables.  Next implement an ordinal scale aligning race and math scores.  Finally, tag the intervals based on race.  Measurements could be viewed using bar charts, line charts, and pie charts.  Other types of graphical outputs also work.

 

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)?

One independent plus one dependent variable references bivariate statistical models.  These remain non-complex (i.e. not multivariate).  Morgan et al offer four types of measurement scales.  They suggest an independent sample or group and repeated measures or or related samples (p. 90).  Some of the tests recommended include: independent samples t Test, Mann-whitney, Wilcoxon, Chi-square, and Mcnear. 

The decision remains data dependent.  Are these normal/scales, ordinal, nominal or other?  Each of these factor into the type of model selected. 

 

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?

Factorial ANOVA (analysis of variance) or multiple regression models address complex problems.  Morgan et al reference multiple regression models are ones where two or more independent variables, and one dependent variable apply (p. 91).  This covers normal or scales, dichotomous data, and all dichotomous.

 

 

References

Morgan, G., Leech, N., Gloeckner, G., Barrett, K. (2020).  IBM SPSS for introductory statistics: Use and interpretation (6th ed.).  Routledge, Taylor et Francis Group. 

Rosenstein, L. D. (2019). Research design and analysis : a primer for the non-statistician. Wiley.