## investigate whether distributions of categorical variables are different from one another, and to conclude if there is an important relationship between the two nominal variables.

Dr. Bill Board designs a 2 X 2 between-subjects factorial design, where Factor A is word frequency (low or high) and Factor B is category cues (no cues or cues). Assume that the data are interval. What type of statistic is needed to analyze the data?
Response 1:
A factorial design is the design that make us know the interaction of factor A* factorB. We can draw the tree as followings;
FactorA: Alow and Ahigh
FactorB: Bno cue and Bcue
Alow ————-Bno cue———–Alow Bno cue
Bcue—————Alow Bcue
Ahigh————Bno cue———–Ahigh Bno cue
Bcue—————Ahigh Bcue
I think we should use two-factor F-test to Analyze. Before we anaylze, we utilize the normality distribution, the Independence between observations and groups and the population variances are equal across factors.
Statistics how to. (2020). ANOVA Test: Definition, Types, Example. Retrieved
from https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/hypothesis-
testing/anova/#FactorialA
Witte, J. & Witte, R. (2017). Statistics (11ed.). Hoboken, NJ: John Wiley & Sons. Retrieved
from https://viewer.gcu.edu/fEk4rR
Response 2:
Topic 8 DQ 2
Denise Hernandez
Chi square statistics to investigate whether distributions of categorical variables are different from one another, and to conclude if there is an important relationship between the two nominal variables. Therefore Chi square is the best test to study the relationship of independence.
References
Witte, R. & Witte, S. (2017). Statistics (11th ed.). Wiley. ISBN-13: 9781119254515

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