m38 problem set STATISTICS

8 Statistical Significance

OK, measures of association are one important thing to examine in data. There is another important thing to consider. If you find associations, are they a result of associations that exist in the population or are those associations simply a result of sampling error? Tests of statistical significance estimate the chances that your associations are a result of the population, and not simply sampling error.

Chi-Square Tests

Chi-Square tests are appropriate for nominal and ordinal variables. When you calculate Chi-Square, you determine the probability that your answer is a result of your sample and not the population. So, a probability of .05 (p = .05) means that the association that you found in your analysis would occur only 5 out of 100 times if there actually was no association in the population. If you had a p = .001, this means that out of 1,000 samples, you would find the association simply as a result of your sampling error 1 time. Convention suggests that probabilities of .05, 01, and .001 support a differing levels of statistical significance of your conclusions.

Let’s go back to our variables SEX and HAPPY. You actually do the same thing that you did when you calculated lambda, except you also check chi-square in the statistics box. Here are the exact steps:

· Analyze > Descriptive Statistics > Crosstabs

· Dependent variable as the Row variable (Mneumonic suggestion: remember DR, dependent belongs on the row)

· Independent variable as the column variable

· Statistics: Lambda or Gamma AND Chi-Square

· Continue > OK

Most of your output will look be the same as when we calculated lambda. There is one new box:

Look at the Asymp. Sig (2 sided). This means that out of 1,000 chances, 883 times you would get the lambda of 0 totally by accident of your sample! Is that statistically significant? Well, not for scientific research. People play the lottery with far worse odds than this, but remember, for a result to be statistically significant in social science research, the probability must be .05 or less.

Let’s think about our query about the relationship between gender and happiness. We have discovered that there is no association between the two and there is no statistical significance. What does that mean? Well, I guess that is a good thing for men and women. It is not a good finding however if you were expecting to find an association between the variables!

T Tests

T tests are used to determine statistical significance of scale (ratio/interval) variables. If you want to examine the associations of nominal/scale variables, you may be quickly overwhelmed with data. If you do discover that you would like to discover the statistical significance of scale variables, I would suggest that you use an Independent-sample t test. You can use your output for the Pearson’s r and it will tell you your level of significance.

Here is the output for our analysis of the association between AGE and SIBS:

SPSS has calculated your t-test for you: Sig. 2-tailed = .019. What does this tell you? It tells you that you would find your association only 19 times out of 1000 due to sample error. Since the significance is less than .05, your association is statistically significant.