Question

2. One personality dimension that seems well recognized by most people is that of introversion-extroversion. Extroverts are described as outgoing, sociable, and fun-loving, whereas introverts are described as reserved and less sociable. Because introverts seem more directed toward their own thoughts and ideas, we might suspect that introverts and extroverts may respond differently to external stimulation such as noise. To more fully investigate this issue, Standing, Lynn, and Moxness (1990) used a 2 ✕ 2 between-subjects design to vary personality type (factor A), introverts and extroverts, and background noise (factor B), quiet and noisy, while subjects performed a reading comprehension task. Suppose you conducted a similar study with 12 subjects per cell, and each person completed a 15 item true-false reading comprehension task. A person’s score was the number of items correctly answered. You obtained the following scores:

	Personality Type (A)
	Introvert	Extrovert
Quiet	10	15
	8	14
	12	12
	15	15
	10	11
	9	8
	14	12
	13	8
	14	13
	7	10
	12	9
	11	11
Background Noise (B)
Noisy	6	13
	8	8
	11	9
	4	14
	5	13
	8	12
	9	15
	10	11
	9	9
	10	11
	7	12
	11	10

2.a.What is the relationship between personality type and the effect of background noise? Use α= .05. If an interaction occurred, use the Tukey HSD test for the simple effects.

2.b.Plot the cell means with the appropriate labelling. You can draw this by hand.

2.c.Report the results as it would appear in a research paper.  

Answer 1

The two factor ANOVA analysis is performed in EXCEL by following these steps;

Step 1: Write the data value in excel. The screenshot is shown below;

Step 2: Data>Data Analysis>Two-Factor With Replication>OK. The screenshot is shown below:

Step 3: Select Input Range: All the data, Rows per sample: 12. For Alpha value = 0.05 at 5% significance level. The screenshot is shown below;

The ANOVA table is obtained. The screenshot is shown below;

a)

From the ANOVA table,

ANOVA
Source of Variation	P-value			Decision
Interaction	0.033232	<	0.05	Significant

The P-value for the interaction between personality type and the effect of background noise is less than 0.05 at 5% significance level. Hence the null hypothesis is rejected. Now, it can be concluded that there is a significant relationship between these two factors.

Tuckey HSD test

Now, to test the significance of simple effects of both the factor, Tuckey HSD test is performed in following steps,

For personality type

The null hypothesis is defined as,

H₀: All the means for personality type are equal

The HSD for each comparison are obtained using the formula,

Where,

The q value is obtained from studentized q distribution table for number of groups, k = 2, degree of freedom = n-k = 48 - 2 = 46 and significance level = 0.05.

The MSE is obtained from the ANOVA for factor personality test,

The decision rule states that if;

From the ANOVA table,

	Introvert	Extrovert
Average	9.708333	11.45833

Since the absolute difference is less than HSD, the null hypothesis is not rejected. It can concluded that there is no simple effect of personality type.

For background noise

The null hypothesis is defined as,

H₀: All the means for background noise are equal

The HSD for each comparison is,

Where,

The q value is obtained from studentized q distribution table for number of groups, k = 2, degree of freedom = n-k = 48 - 2 = 46 and significance level = 0.05.

The MSE is obtained from the ANOVA for factor personality test,

From the ANOVA table,

	Average
Quiet	11.375
Noise	9.791667

Since the absolute difference is less than HSD, the null hypothesis is not rejected. It can concluded that there is no simple effect of noise type.

b)

	Introvert	Extrovert	Average
Quiet	11.25	11.5	11.375
Noise	8.166667	11.41667	9.791667
Average	9.708333	11.45833

The plot is obtained in excel. The screenshot is shown below,

c)

Interaction: The parallel plot shown no interaction while non parallel plot shows interaction between two groups. From the plot we can see that there is an interaction between two groups personality type and background noise.

Simple effect: For each line we can see that there is a very small difference between the groups of Quiet and and Noise as well which indicate very little of no simple effect.