Week 6 Review Questions
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Topic 6 Review Questions
Kaarthik Chandrashaker
College of Humanities and Social Sciences, Grand Canyon University
PSY 520: Graduate Statistics Dr. Jim Dudleston July 12, 2023
2
16.9 Given the aggression scores below for Outcome A of the sleep deprivation experiment,
verify that, as suggested earlier, these mean differences shouldn’t be taken seriously by testing
the null hypothesis at the .05 level of significance. Use the computation formulas for the various
sums of squares and summarize results with an ANOVA table.
Given df between = 2 ^ df within = 6
SS
SS between= ∑T 2 /n - G 2/N
[ (15)2/3 + (18)2/3 + (12) 2/3] – (45) 2/9
[ 225/3 + 324/3 + 144/3] -2025/9=
[75 + 108 + 48] – 225 = 231 – 225 = 6
SS within= ∑ x2- ∑T2/n
(3)2 + (5)2 + (7)2 + (4)2 + (8)2 + (6)2 + (2)2 + (4)2 + (6)2 – [ (15)2/3 + (18)2/3 + (12) 2/3 ]
= 9+25+49+16+64+36+4+16+36 – [75+108+48]
=255-231=24
SS total
= ∑x2
-G2/N
255-225=30
30=6+24
18.12
A) sscolumn
[ (25)2 /8 + (30)2 /8 + (64) 2/ 8 + (67) 2 /8 ]− (186 )2/32
[ 625/8 + 900/8 + 4096/8 + 4489/8 ] − 34596/32
3
[78.13 + 112.5 + 512 + 561.13] – 1081.13
Df column= 3
SS row
[ 841/8 + 1296/8 + 2809/8 + 4624/8 ] – 34596/32
[105.13 + 162 + 351.13 + 578] – 1081.13
1196.26 – 1081.13 = 115.14
SSbetween
1466 – 1399 = 67
Dfwithin= n- (c) (r)
32 – (4) (4) = 32 – 16 =16
SSinteraction=SSbetween – (SScolumn + SSrow)
317.87 – [182.63 + 115.14] 317.87 – 297.77 = 20.10
Dfinteraction = 9
ANOVA
Source of Variation SS df MS F p-value F crit
Sample: alcohol 115.123 3 38.375 9.164179104 0.000918419 3.238871517
Columns: sleep 182.625 3 60.875 14.53731343 7.84492E-05 3.238871517
Interaction 20.125 9 2.236111111 0.533996683 0.829228202 2.537666539
Within 67 16 4.1875
Total 284.875 31
There is an effect for alcohol because F =9.164 which is larger than F crit =3.239.
There is an effect for Sleep Deprivation because F= 14.537 which is larger than F crit 3.239.
There is no interaction between alcohol consumption and Sleep Deprivation because F=0.534
which is less than F crit =2.538.
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B) Effect size = SS effect / SS total Alcohol Consumption: effect size = 115.125 / 384.875 = 0.299. The effect size is small.
Sleep Deprivation: effect size = 182.625 / 384.875 = 0.475 The effect size is medium.
interaction: effect size = 20.125 / 384.875 = 0.052 This effect size is medium.
Tukey’s HSD Test
Difference of means 0hrs 24hrs 48hrs 72hrs
0hrs 0 0.625 4.875 5.25
24hrs 0 4.25 4.625 48hrs 0 0.375 72hrs 0 q= 4.05
HSD=2.930134
Only the means for 48 and 72 hours show a significant effect