ANOVA Measures: Advertising and Customers’ Behavior

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Table of Contents

Statistics
Application of Analytical Strategy
Reference

Statistics

Exploratory Data Analysis

Figure 1: The Proportions of Gender.

Table 1. Descriptive Statistics of Test Scores
		Pre-test score	Week 2 score	Week 4 score	Week 6 score	Week 8 score	Week 10 score	Week 12 score
N	Valid	12	12	12	12	12	12	12
N	Missing	0	0	0	0	0	0	0
Mean		29.58	33.08	35.42	35.67	39.92	45.67	50.00
Median		28.00	31.50	34.00	37.00	39.00	45.50	49.00
Mode		20	25	28^a	39	39	47^a	58
Std. Deviation		12.221	10.113	9.885	10.671	9.718	8.690	10.189
Variance		149.356	102.265	97.720	113.879	94.447	75.515	103.818
Skewness		1.254	1.797	2.199	.771	1.483	1.119	.769
Std. Error of Skewness		.637	.637	.637	.637	.637	.637	.637
Kurtosis		1.889	4.305	5.778	1.363	3.676	2.747	1.359
Std. Error of Kurtosis		1.232	1.232	1.232	1.232	1.232	1.232	1.232
Range		43	38	36	40	37	34	39
Minimum		16	22	27	20	28	33	34
Maximum		59	60	63	60	65	67	73

Pie chart (Figure 1) depicts that the proportion of males (33.33%) is less than that of females (66.67%). Descriptive statistics (Table 1) indicate that the test scores increase with the duration of learning. The means of test scores increased from the baseline of 29.58 (SD = 12.22) in the first week to 33.08 (SD = 10.11), 35.42 (SD = 9.89), 35.67 (SD = 10.67), 39.92 (SD = 9.72), 45.67 (SD = 8.69), and 50.00 (SD = 10.19) in 2, 4, 6, 8, 10, and 12 weeks, respectively. Therefore, descriptive statistics demonstrate that the duration of learning improves the performance of students.

Repeated Measures ANOVA

Table 2 shows that time and gender vary with test scores among participants. The means of test scores not increase with time but also those of males are greater than those of females.

Table 2. Descriptive Statistics
	Gender	Mean	Std. Deviation	N
Pre-test score	Female	28.25	8.172	8
	Male	32.25	19.432	4
	Total	29.58	12.221	12
Week 2 score	Female	29.75	6.319	8
	Male	39.75	13.889	4
	Total	33.08	10.113	12
Week 4 score	Female	33.63	5.181	8
	Male	39.00	16.432	4
	Total	35.42	9.885	12
Week 6 score	Female	35.88	6.556	8
	Male	35.25	17.802	4
	Total	35.67	10.671	12
Week 8 score	Female	39.38	5.370	8
	Male	41.00	16.633	4
	Total	39.92	9.718	12
Week 10 score	Female	44.88	5.743	8
	Male	47.25	13.961	4
	Total	45.67	8.690	12
Week 12 score	Female	48.38	8.518	8
	Male	53.25	13.793	4
	Total	50.00	10.189	12

The analysis of data (Table 3) shows that it violates the assumption of sphericity because it rejects the hypothesis that variances of test scores are equal, χ²(20) = 56.876, p = 0.000. The violation of the assumption of sphericity inflates F-ratio and increases the probability of type I error (Field, 2018). In instances where there is a violation of the assumption of sphericity, interpretation of results requires the use of Greenhouse-Geisser correction.

Table 3. Mauchly’s Test of Sphericity^a
Within-Subjects Effect	Mauchly’s W	Approx. Chi-Square	df	Sig.	Epsilon^b
					Greenhouse-Geisser	Huynh-Feldt	Lower-bound
Time	.001	56.876	20	.000	.441	.674	.167

Repeated measures ANOVA based on Greenhouse-Geisser correction (Table 4) shows that gender has no main effect on the test scores of participants due to the lack of statistically significant interaction effect. Post hoc analysis is not possible in this case because gender is a variable with two categories. Time has a statistically significant main effect because it increases with test scores, F(2.646, 26.456) = 20.609, p = 000. Post hoc tests are not applicable here because test scores is a within-subject variable. Overall, time and gender has no statistically significant interaction in influencing variation in test scores, F(2.646, 26.456) = 1.156, p = 0.341.

Table 4. Tests of Within-Subjects Effects of Time and Gender.
Source		Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared
Time	Sphericity Assumed	3246.536	6	541.089	20.609	.000	.673
	Greenhouse-Geisser	3246.536	2.646	1227.164	20.609	.000	.673
	Huynh-Feldt	3246.536	4.045	802.659	20.609	.000	.673
	Lower-bound	3246.536	1.000	3246.536	20.609	.001	.673
Time * Gender	Sphericity Assumed	182.155	6	30.359	1.156	.342	.104
	Greenhouse-Geisser	182.155	2.646	68.853	1.156	.341	.104
	Huynh-Feldt	182.155	4.045	45.035	1.156	.344	.104
	Lower-bound	182.155	1.000	182.155	1.156	.307	.104
Error(Time)	Sphericity Assumed	1575.321	60	26.255
	Greenhouse-Geisser	1575.321	26.456	59.546
	Huynh-Feldt	1575.321	40.447	38.948
	Lower-bound	1575.321	10.000	157.532

Application of Analytical Strategy

My research area of interest is the influence of the duration of advertising on the purchasing behavior of customers. The duration of advertising, persuasiveness, and gender are three variables that I would employ in repeated measures ANOVA. The duration of advertising is an independent variable that exists on a continuous scale of the number of days. In contrast, persuasiveness is a dependent variable measured on an ordinal scale based on a 10-point Likert scale. As a demographic variable, gender is on a categorical scale comprising males and females. Persuasiveness is a repeated measure assessed daily for one week as per the duration of advertising, whereas gender is a fixed factor.

In SPSS output, I would look at the table of Mauchly’s test of sphericity to determine if the variance of persuasiveness violated the assumption of sphericity. Specifically, chi-square value and p-value would determine if variation in persuasiveness in different days of advertising is equal. If the data do not violate the assumption of sphericity, it implies that F-ratio is accurate and the probability of type I error is low.

Reference

Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). New York, NY: SAGE Publications.

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ANOVA Measures: Advertising and Customers’ Behavior

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