To test whether arousal or stress levels increase as the difficulty of a task in
ID: 3369764 • Letter: T
Question
To test whether arousal or stress levels increase as the difficulty of a task increases, 24 participants (n = 8; N = 24) were randomly assigned 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 (µS), with higher signals indicating greater arousal or stress. The data for each task are given in the table. Using the .05 significance level, did stress increase with task difficulty
What is the independent variable?
What are the levels of the IV?
Is this a between or within subjects research design? Explain.
What is the dependent variable?
What is the operational definition of the dependent variable?
Is this an experimental or quasi-experimental research design? Explain.
If this were an actual research study, what threats to validity would we be most concerned about? How could we control for them?
Use the steps of hypothesis testing to evaluate this hypothesis.
State the hypotheses.
Determine the critical value of your statistic for rejecting the null based on the given alpha level/sample size.
Calculate the statistic.
Based on this statistic alone, would you reject or accept the null hypothesis?
Calculate both effect size statistics. What do these mean?
Using the Omega Squared statistic, determine the power of the study. What does this mean?
If the ANOVA result is significant, calculate Tukey’s HSD to determine which groups are significantly different?
Write an APA formatted results section for this study, including appropriate tables and graphs. In a full paper format, tables and graphs would come at the end of the manuscript. However, for this assignment, you can imbed them where appropriate.
Easy Tical Difficult 2.6 1.0 5.6 3.9 45 5.6 3.4 3.7 3.5 1.2 27.8 2.1 33 64 1.2 4.6 75 1.8 31 4.4Explanation / Answer
Use the steps of hypothesis testing to evaluate this hypothesis.
State the hypotheses.
Here we have to test,
H0 : All means are equal.
H1 : Atleast one mean differ.
Descriptive statistics of your k=3 independent treatments:
One-way ANOVA of your k=3 independent treatments:
Conclusion from Anova:
The p-value corresponing to the F-statistic of one-way ANOVA is lower than 0.05, suggesting that the one or more treatments are significantly different. The Tukey HSD test follow. These post-hoc tests would likely identify which of the pairs of treatments are significantly differerent from each other.
Tukey HSD Test:
The p-value corrresponing to the F-statistic of one-way ANOVA is lower than 0.05 which strongly suggests that one or more pairs of treatments are significantly different. You have k=3 treatments, for which we shall apply Tukey's HSD test to each of the 3 pairs to pinpoint which of them exhibits statistially significant difference.
We first establish the critical value of the Tukey-Kramer HSD Q statistic based on the k=3 treatments and ?=21 degrees of freedom for the error term, for significance level ?= 0.05 (p-values) in the Studentized Range distribution. We obtain these ctitical values for Q, for ? of 0.05,
Qcritical?=0.05,k=3,?=21 = 3.5636
We calculate a parameter for each pair of columns being compared, which we loosely call here as the Tukey-Kramer HSD Q-statistic, or simply the Tukey HSD Q-statistic, as:
Qi,j = |x¯i?x¯j| / si,j
where the denominator in the above expression is:
si,j = ?^? / sqrt(Hi,j) ????i,j=1,…,k;i?j
The quantity Hi,j is the harmonic mean of the number of observations in columns labeled i and j. Note that when the sample sizes in the columns are equal, then their harmonic mean is simply the common sample size. When the sample sizes of columns in a pair being compared are different, the harmonic mean lies somewhere in-between the two sample sizes. The relvant harmonic mean is required for applying the Tukey-Kramer procedure for columns with unequal sample sizes. The quantity ?^? = 1.4852 is the square root of the Mean Square Error = 2.2057 determined in the precursor one-way ANOVA procedure. Note that ?^? is same across all pairs being compared.
The test of whether the NIST Tukey-Kramer confidence interval includes zero is equivalent to evaluating whether Qi,j>Qcritical, the latter determined according to the desired level of significance ? (p-value), the number of treatments k and the degrees of freedom for error ?, as described above.
post-hoc Tukey HSD Test Calculator results:
Tukey HSD results
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We can see that pair A,B is insignificant while last two pairs are significant.
Treatment ? A B C Pooled Total observations N 8 8 8 24 sum ?xi 18.4000 28.8000 48.0000 95.2000 mean x¯ 2.3000 3.6000 6.0000 3.9667 sum of squares ?x2i 48.9000 114.9600 316.4600 480.3200 sample variance s2 0.9400 1.6114 4.0657 4.4649 sample std. dev. s 0.9695 1.2694 2.0164 2.1130 std. dev. of mean SEx¯ 0.3428 0.4488 0.7129 0.4313Related Questions
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