A researcher is interested in studying persuasiveness; in particular, which aspe
ID: 3313201 • Letter: A
Question
A researcher is interested in studying persuasiveness; in particular, which aspects of a message make it more or less persuasive. She decides to look at the volume of the message – does a louder message make you pay more attention than a quieter message? To address this question, she presented participants with a recorded political campaign commercial at one of three volumes (quiet, “normal,” and loud). Additionally, she decides to examine whether there are differences in persuasion between males and females. Participants rated the commercial on persuasiveness, with higher scores indicating greater persuasiveness. Below is a copy of the source table that the researcher obtained with a statistics computer program; however, her printer malfunctioned and she is missing some of the entries…
Source
SS
df
MS
F
Volume
58.73
Gender
93.39
Volume x Gender
102.77
Within
12
8.22
--
Total
412.28
17
--
--
Complete the source table for the researcher. Using the source table, what do you conclude about the effects by looking at the F values?
Source
SS
df
MS
F
Volume
58.73
Gender
93.39
Volume x Gender
102.77
Within
12
8.22
--
Total
412.28
17
--
--
Explanation / Answer
Solution:
Calculations, formulas, and completed table are given as below:
SS within = MS within * df within = 8.22*12 = 98.64
SS volume = SS total – SS gender – SS volume x gender – SS within
SS volume = 412.28 – 93.39 – 102.77 – 98.64 = 117.48
df volume = SS volume / MS volume = 117.48 / 58.73 = 2 approximately
Total number of genders = 2
df for gender = 2 – 1 = 1
df for volume x gender = df volume * df gender = 2*1 = 2
MS = SS/df
MS gender = 93.39 / 1 = 93.39
MS volume x gender = 102.77/2 = 51.385
F = MS treatment / MS within
F for volume = 58.73/8.22 = 7.144768856
F or Gender = 93.39 / 8.22 = 11.36131387
F for volume x gender = 51.385 / 8.22 = 6.251216545
P-values are calculated by using F-table or excel. Completed ANOVA table is given as below:
Source
SS
df
MS
F
P-value
Volume
117.48
2
58.73
7.144768856
0.009044609
Gender
93.39
1
93.39
11.36131387
0.005563467
Volume x Gender
102.77
2
51.385
6.251216545
0.01379851
Within
98.64
12
8.22
--
Total
412.28
17
--
--
Volume, Gender, and their interaction are statistically significant at 5% level of significance as the p-values are less than = 0.05.
Source
SS
df
MS
F
P-value
Volume
117.48
2
58.73
7.144768856
0.009044609
Gender
93.39
1
93.39
11.36131387
0.005563467
Volume x Gender
102.77
2
51.385
6.251216545
0.01379851
Within
98.64
12
8.22
--
Total
412.28
17
--
--
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