Chi square

Chi square

1. non-parametric test can be used as an alternative to parametric tests.

   • Non-parametric tests make no assumptions about population parameters (i.e. they are distribution free tests)

2. non-parametric tests can use data at a nominal level

3. Non-parametric test are not as powerful as parametric statistical tests

4. chi square does something quite simple. We count up how often something happend and first tells us if we saw what we expected to see

5. used in unrelated data. Every participant/ case yields data for only one catergory

6. used to answer questions about the proportions of a popular distribution

7. used to compare different levels of one variable

8. compares the sample proportions to population proportions as specified by hthe null hypothesis

9. The observed frequencies are numbers of participants measured in individual catergpries

   • These frequencies are then compared to frequencies predicted by the null hypothesis (the expected frequencies)

10. catergorical data are different: we have catergorical data when people can only belong to a limired number of groups

11. So we conclude that there are significantly more men in the computing department than would be expected by chance: X (1) = 4.55, p<.05

12. how to work out the df in the chi square test of independence (R-1)x(C-1) =2-1x 2-1 = 1

    • critical value is 3.84 which means the p value is 0.5

13. Chi- Squared Goodness of Fit

    • You have a few different group - the null hypothesis is the idea that there will be more or less the same number of people in each group whilst the alternative hypothesis is there will be more people in the same groups
      • We can choose between those two idea. We start by working out how many people we would expect to see in each age group if the null hypothesis was correct. Then we count up how many people actually fall into each age group
        • THE SUM OF: (observed - expected) squared / expected

14. Chi Squared Test of Independence

    • Are two seperate variables independent or associated
    • As with the GF the TI use data in the form of frequencies in different catergories, which is compared to expected frequencies prediicted from the null hypothesis
    • The null hypothesis states that the two variables being measured are completely independent from each other: they do not affect eachother at all
    • the expected frequencies are worked out using this formula: column total x row total / total sample
      • once you work this out for each catergory you use the same formula for the goodness of fit test: THE SUM OF: (observed - expected) squared / expected
        • THE DIFFERENCE BETWEEN THE TWO CHI-SQUARED TESTS IS THE WAY YOU WORK OUT THE EXPECTED FREQUENCIES
          • CHI- SQAURED TEST OF INDEPENDENCE LOOKS AT TWO GROUPS