Question

ADC supermarket accepts three types of credit cards, Master card, Visa and Tembo card. The sales manager is interested in finding out whether there is a difference in the mean amounts charged by customers on the three cards. A random sample of 18 credit cards purchases revealed these credit card amounts. At the level of 0.05, using ANOVA test can we conclude that, there is a difference in the mean amounts charged per purchase on the three cards? Would Tukey-Kramer test be appropriate? Why? Master card 61 28 42 33 51 56 Visa card 85 56 44 72 98 56 72 Tembo card 61 25 42 31 29

Answer 1

To perform the Tukey-Kramer (T-K) multiple comparisons procedure first one way ANOVA analysis is performed in excel by using following steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > ANOVA: single Factor > OK.  The screenshot is shown below,

Step 3: Select Input Range: All the data values column, Alpha = 0.05. The screenshot is shown below,

The result is obtained.  The ANOVA table is shown below,

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	3337.967	2	1668.983	6.629907	0.008648	3.68232
Within Groups	3776.033	15	251.7356
Total	7114	17

Post-Hoc test

Now, the Tukey-Kramer (T-K) multiple comparisons procedure is used to test all the pairwise comparison and identify which pair is significantly different.

The Tukey-Kramer method uses the formula,

Where, k is the number of groups.

From the ANOVA table, k = 3,

The q value is obtained using the q distribution table for significance level = 0.05, number of groups, k = 3, degree of freedom = N - k = 18 - 3 = 15.

The HSD value for group 1 and 2 comparison ,

The HSD value for group 1 and 3 comparison ,

The HSD value for group 2 and 3 comparison ,

Now,

The mean value for each groups are,

Groups	Average
Master card,	45.16667
Visa card,	69
Tembo card,	37.6

There are 3 possible comparison as follows,

Comparison	Difference		HSD
	-23.8333	>	22.92584	Significant
	7.5667	<	24.95249	Significant
	31.4	>	24.12875	Significant