Question

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

1.

Given table data is as below MATRIX col1 col2 TOTALS row 1 99 85 184 row 2 95 70 165 TOTALS 194 155 N = 349 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formula E-TABLE col1 col2 row 1 102.281 81.7192 row 2 91.7192 73.2808 ------------------------------------------------------------------ calculate chi square test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 99 102.281 -3.2808 10.764 0.1052 85 81.7192 3.2808 10.764 0.1317 95 91.7192 3.2808 10.764 0.1174 70 73.2808 -3.2808 10.764 0.1469 ᴪ^2 o = 0.5012 ------------------------------------------------------------------ set up null vs alternative as null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent level of significance, α = 0.05 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =3.8415 since our test is right tailed,reject Ho when ᴪ^2 o > 3.8415 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 0.5012 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.8415 we got | ᴪ^2| =0.5012 & | ᴪ^2 α | =3.8415 make decision hence value of | ᴪ^2 o | < | ᴪ^2 α | and here we do not reject Ho ᴪ^2 p_value =0.479 ANSWERS --------------- null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent test statistic: 0.5012 critical value: 3.8415 p-value:0.479 decision: do not reject Ho

we do not have enough evidence to support the claim that possible interaction in this experiment

2.

the results of this experiment would lead you to be hesitant to interpret an interaction, if one were present in this experiment then it is possible to support the claim.  

3.

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 researcher modify the experiment so as to be able to interpret an interaction.