Question

To test whether arousal or stress levels increase as the difficulty of a task increases, eight participants were asked to complete an easy, typical or difficult task. Their galvanic skin response (GSR) was recorded. A GSR measures the electrical signals of the skin in units called microSiemens, with higher signals indicating greater arousal or stress.

a. Write the null hypothesis in symbols and words

b. Write the alternative hypothesis in symbols and words

c. By hand, calculate each degrees of freedom. Show calculations.

d. Use the anova function in R to obtain the test statistic and p-value. Report the ANOVA table.

e. Make a decision about the null using the p-value approach.

f. If appropriate, calculate and interpret the effect size. If not, state why.

g. Use R to conduct a post hoc analysis and interpret results.

h. Write the conclusion in APA style.

Difficulty Stress Easy 2.6 Easy 3.9 Easy 3.4 Easy 1.2 Easy 2.1 Easy 1.2 Easy 1.8 Easy 2.2 Typical 5.6 Typical 4.5 Typical 3.7 Typical 2.0 Typical 3.3 Typical 4.6 Typical 3.1 Typical 2.0 Diff 9.0 Diff 5.6 Diff 3.5 Diff 7.8 Diff 6.4 Diff 7.5 Diff 4.4 Diff 3.8

Answer 1

a)
Null hypothesis, ho: there is no significant difference in the mean stress between three types of difficulty. u1=u2=u3

b)
Alternative hypothesis, h1: at least one of the mean stress between three types of difficulty differ significantly. u1 =/= u2 =/= u3

c)
df_regression = (k-1) = 3-1 = 2
df_total = n-1 = 24-1 = 23
df_error = n-k = 24-3 = 21

d)

test statistic = 12.78
p-value = 0.000234

e)
Since p<5%, i reject Ho at 5% level of signficance. there is sufficient evidence to support the claim at least one of the mean stress between three types of difficulty differ significantly. u1 =/= u2 =/= u3

f)
Eta sq = SS_effct/(SS_effct+SS_error)
Eta sq = 56.37/(56.37+46.32)
Eta sq = 0.548933684
Moderate effect

g)

Since p<5%, I can say that there is a significant difference in the mean stress between (Easy, diff) and (Typical-Diff).