SPSS exercise 3.2

The SummoScanner is the continuous survey of print media penetration. This exercise is about the target group research in 1998, for which a random sample of the Dutch population of those aged 13 years and older was taken. The respondents in the Summo surveys are asked to state, in relation to a large number of newspapers and magazines, whether they 1) ever read or browse through them, 2) whether they have read or browsed through the most recent edition, and 3) how many of the past six editions they have read or browsed through. Based on the answers to the last two questions, a so-called reading likelihood is calculated (the names of these variables all start with rc_). The variables are measured at interval level.

Database: Summo.Readingchance.sav

a. Test the hypothesis that there is a greater likelihood of men reading a national newspaper (rc_natnews) than women.

We can test this hypothesis by comparing the average likelihood of men reading a newspaper with that of women. The test we use for this is the t-test. As we can imagine that we can take separate samples for men and for women, these are independent scores. We must therefore use the t-test for the difference between two averages (independent samples). We must first describe the variables and assess whether there are any errors in the data that we need to rectify, and do the data meet the conditions for a t-test?

There are no impossible values with the reading likelihood. The sample is large enough (N > 100) to carry out the t-test, even though the variable in the population has a somewhat skewed distribution (the skewness in the sample is 0.47).

Group Statistics

Gender N Mean Std. Deviation Std. Error Mean

Reading chance national newspapers Male 5050 ,4324 ,37710 ,00531

Female 6756 ,3201 ,35571 ,00433

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means

F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference

Lower Upper

Reading chance national newspapers Equal variances assumed 127,311 ,000 16,539 11804 ,000 ,11230 ,00679 ,09899 ,12561

Equal variances not assumed

16,400 10520,219 ,000 ,11230 ,00685 ,09887 ,12572

We can see that on average, men are more likely to read a national newspaper (M = 0.43, SD = 0.38) than are women (M = 0.32, SD = 0.36). To further assess the differences, you first need to know whether the two group's variances are equal in the population. Failure to adhere to this assumption will generally increase the chance of making a Type I error (thus detecting an effect that is not present). You need to consult the "Sig." column located under the "Levene's Test for Equality of Variances" column. In this case, the significance value is ".000" (i.e., p = .000). If the population variance of both groups is equal, this test will return a p-value greater than 0.05 (i.e., p > .05), indicating that you have met the assumption of homogeneity of variances. However, if the test returns a p-value less than 0.05 (p < .05), the population variances are unequal and the data have violated the assumption of homogeneity of variances. In this example, the population variances of the engagement scores for both groups are not equal because p = .000 (i.e., p < .05). Therefore, the assumption of homogeneity of variances is not met and you need to interpret the bottom row of the table (Equal variances not assumed). The difference is statistically significant, t (10,520.22) = 16.40; p < 0.001 unilateral; 95% CI [0.10, 0.13]; d = 0.31.

The effect size with this difference is small to medium: see the calculation below, where the pooled variance is first calculated:

and

The null hypothesis that men are no more likely to read a national newspaper (H₀: μ_men ≤ μ_women) can therefore be rejected and the research hypothesis can therefore provisionally be assumed.

*SYNTAX
*Describing variables.
FREQUENCIES
  VARIABLES=gender
  /ORDER= ANALYSIS .
EXAMINE
  VARIABLES=rc_natnews
  /PLOT BOXPLOT
  /COMPARE GROUP
  /STATISTICS DESCRIPTIVES
  /CINTERVAL 95
  /MISSING LISTWISE
  /NOTOTAL.
*T-test for independent scores.
T-TEST
  GROUPS = gender(1 2)
  /MISSING = ANALYSIS
  /VARIABLES = rc_natnews
  /CRITERIA = CI(.95) .

b. Test the hypothesis that the Dutch are as likely to read a national newspaper as they are a regional one (rc_regnews).

c. Select several background characteristics of the respondents that you would expect to affect the likelihood of their reading a regional newspaper. Use a t-test to see if your expectation is borne out. Note: if necessary, always put the background characteristics into two categories, providing your arguments for doing so.