Question

Question: A researcher has used a complex design to study the effects of caffeine (caffeinated and decaffei...

A researcher has used a complex design to study the effects of caffeine (caffeinated and decaffeinated) and problem difficulty (easy and hard) on subjects’ memories. The researcher tested a total of eighty subjects, with twenty subjects randomly assigned to each of the four groups resulting from the factorial combination of the two independent variables. The data presented in the table represent the percentage words that subjects recalled correctly in each of the four conditions.

Caffeine
Problem difficulty	Caffeinated	Decaffeinated
Easy	99	85
Hard	95	70

1. Is there evidence of a possible interaction in this experiment?

2.What aspects of the results of this experiment would lead you to be hesitant to interpret an interaction, if one were present in this experiment?

3.How could the researcher modify the experiment so as to be able to interpret an interaction if it should occur?

Answer 1

Hello ,

1. Is there evidence of a possible interaction in this experiment?

There are several types of chi square tests depending on the way the data was collected and the hypothesis being tested. We'll begin with the simplest case: a 2 x 2 contingency table. If we set the 2 x 2 table to the general notation shown below in Table 1, using the letters a, b, c, and d to denote the contents of the cells, then we would have the following table:

Table 1. General notation for a 2 x 2 contingency table.

Variable 2	Data type 1	Data type 2	Totals
Category 1	a	b	a + b
Category 2	c	d	c + d
Total	a + c	b + d	a + b + c + d = N

For a 2 x 2 contingency table the Chi Square statistic is calculated by the formula:

	Caffeinated	Decaffeinated	Marginal Row Totals
Easy	99   (102.28)   [0.11]	85   (81.72)   [0.13]	184
Hard	95   (91.72)   [0.12]	70   (73.28)   [0.15]	165
Marginal Column Totals	194	155	349    (Grand Total)

The chi-square statistic is 0.5012. The p-value is .478978. This result is not significant at p < .05.

The chi-square statistic with Yates correction is 0.3601. The p-value is .54847. Not significant at p < .05.

3.How could the researcher modify the experiment so as to be able to interpret an interaction if it should occur?

We can add one more categore in the analysis like median, Easy Median and hard.