Section 8.4: Nominal Dependent Variable
From Research Methods in Psychology
Contents |
[edit] Introduction
Nominal data are the simplest type of data, they count the number of individuals in the different categories. Analysis of simple experiments that have a nominal dependent variable is straightforward, surprisingly, in complex experiments this analysis becomes much more complex.
[edit] One Independent Variable
[edit] Independent Groups
If you have carried out an experiment that used an independent groups design, your data will consist of a contingency table. For example, you could carry out a study to investigate the effectiveness of a marketing campaign. When customers entered a travel agent asking about a holiday, some customers would be randomly selected, and offered free insurance for their holiday. The independent variable is whether the customer was offered free insurance, and the dependent variable is whether the customer bought the holiday, or not.
We can represent the results of the study in a contingency table, shown below. Of 100 people who were offered free insurance, 65 bought a holiday. Of 100 people who were not offered free insurance, 52 bought a holiday. We are interested in testing the null hypothesis that offering free insurance makes no difference to the probability that someone would buy a holiday.
|
Bought a Holiday | ||||
|---|---|---|---|---|
| Yes | No | Total | ||
|
Offered free insurance? | Yes | 65 | 35 | 100 |
| No | 52 | 48 | 100 | |
| Total | 117 | 83 | 200 | |
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Concept: A chi-squared test is used to compare two or more groups when the dependent variable is nominal. |
To test this hypothesis, we carry out a chi-square (the Greek letter ‘chi’ is pronounced ‘ky’ – like ‘sky’, but without the ‘s’.) When you report a chi-squared test, you should report the value for 2, the df, and the associated p value. In the case of the data presented in Table 4, we find that chi-square = 3.48, df=1 and p=0.062, so, because the value for p is greater than 0.05, we therefore cannot reject the null hypothesis that offering a free holiday does not have any effect.
The chi-squared test makes the following assumptions of your data:
- Count Each Person Once Only. Every person must only make one contribution to the contingency table. If they make more than one contribution, the 2 is invalid. For example if our dependent variable was whether the person ate chips or salad, and we counted someone separately under both chips and salad (thus counting that person twice), we could not analyse the data using 2 .
- Expected Values Less Than 5. If you calculate 2 by hand, you will calculate expected values. Alternatively if you use a computer, the expected values should be reported by the computer. For the test to be valid, at least 80% of the expected values in a contingency table must exceed 5. If they do not exceed 5, you can use Fisher’s Exact Test.
[edit] Three or More Levels of Independent Variable
The 2 test for a contingency table generalises to a table which has more than two levels of the independent variable, and more than two possible outcomes for the dependent variable. We could carry out an experiment further examining people’s behaviour in the travel agents. As well as offering them free insurance, we could offer free children’s places on the holiday. In addition to just looking at whether they bought a holiday, we could see if they took brochures away or not. Our contingency table for this study would have three rows (offered nothing, free insurance or free child places) and three columns (bought nothing, took brochure away, bought holiday).
Action
Bought Took Bought Total
nothing brochures holiday
Offered
Nothing 105 120 75 300
Free
insurance 85 140 75 300
Free 75 100 125 300
child places
Total 265 360 275 900
The chi-squared value is now equal to 30.1, with 4df, p < 0.0001, and because the p value is less than 0.05, we can reject the null hypothesis that there is no difference between the three conditions of the independent variable.
If you analyse a contingency table which is larger than 22 using a chi-squared test, you must still make the assumption that 80% of the expected values are greater than 5. Unfortunately if your table is not a 2x2 table, you cannot carry out a Fisher’s exact test. Some computer programs will allow you to do something called an ‘exact test,’ but these are rather complex – the better option is to collect data from a larger sample.
We saw that when we had an interval dependent variable, it was possible to further explore the data using post-hoc tests. It is possible to further explore the data from a contingency table using post-hoc tests, but it is difficult and very rarely done – the procedure is described in Everitt (1992).
[edit] Within Participants Design
[edit] Two Levels of Independent Variable
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Concept: McNemar’s test and the Sign test used in a within-participants experiment which has one independent variable, which has two levels, and a dependent variable which can take on one of two values. |
If you are designing a repeated measures study that has a nominal dependent variable, you are limited in the choices that you can make. The dependent variable must be dichotomous – that is it must only be able to take on two values. If you do not stick to this restriction, you will find it very difficult to analyse your data. There are two similar tests that can be used, the Sign Test and McNemar’s test.
The sign test gives a value of either S or Z (if you calculate it by hand, you will probably use S, most computer programs give Z). It is reported as Z=2.69, p=0.007. McNemar’s test gives a chi-square, and is reported as chi-square =7.2, N=262, p=0.007.
[edit] Three or more levels of independent variable
If you have a repeated measures design in which there are three levels of the independent variable, you must ensure that the dependent variable is dichotomous – that is, it can only take on one of two values. If the dependent variable is not dichotomous, you can carry out a Cochran’s Q test. When you carry out this test you should report Q, the df and the p value.
[edit] More Than One Independent Variable
Experiments which have a nominal dependent variable and more than one independent variable are very difficult to analyse, and it is unlikely that you will cover the appropriate analyses for this in your degree studies.
If you have an independent groups design, and have more than one independent variable, you need to logistic regression analysis.
