## Balanced One-Way ANOVA

### Example Problem

[Podcast~9 minutes]

A direct marketer of insurance wanted to evaluate the effect of age on the response rate to a new insurance product. Below are the response rates per 1,000 mailings by group from 12 different metropolitan areas.

Table 1

Response Rate Per One Thousand Mailings

 Young Middle Elderly 25 30 25 27 29 22 23 29 27 24 31 23 23 28 24 24 31 25 22 29 23 25 32 22 21 30 21 24 29 22 21 28 24 23 31 23

### SPSS Analysis

Dataset

Screen Data

Accuracy of data, normality and outliers within each group needs to be examine.

Running Analysis

Output

We do not want to reject this Ho & we didn't.

Post Hoc (Tukey)
If you reject Ho, you need to find where the differences are occurring.
In this example differences are found between Young and Middle, and Middle and Elderly.

Results

Prior to running the major analysis, all variables were examined for accuracy of data entry, outliers, missing values, normality of distribution and homogeneity of variance. All data were in acceptable ranges with no outliers found (i.e., greater than 3 standard deviations away from the mean), and there were no missing values. A visual inspection of the distribution for each group and the values for skewness, which were all less than the absolute value of 1.0, suggested a reasonably normal distribution.

The means and standard deviations by age groups are reported in Table 1. The Levene's test for homogeneity of variances was not statistically significant suggesting that the three groups had equivalent variances. A one-way analysis of variance yielded a significant difference among the age group means, F(2, 33)=63.60, p<.001. A post hoc analysis using Tukey's procedure (a =.05) indicated that the mean for the middle age group was significantly higher than the young and elderly age groups. There was no significant difference between the means of the young and elderly groups.

Discussion

The results indicate a significantly higher response rate from the middle age group for this particular insurance product.