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3003psy week 10

Terms in this set (16)

What is a chi-square test?
Used for frequency data, allows testing of research with categorical data.
Can ask research questions like: are people/things distributed evenly across the categories of this variable?
What do chi-square analyses involve?
Working out expected likelihood of something happening (what frequencies you should get if the null hypothesis is true) and comparing it with the observed frequencies (what frequencies you do get)
What do one-way chi-square tests tell you?
How well expected and observed frequencies match - also known as the 'goodness of fit' test.
How do you interpret the result of a one-way chi square analyses and see if null hypothesis has been violated?
Find the critical value for p = 0.5, where null hypothesis is true, dependant on the degrees of freedom calculated using k - 1. If obtained chi-square is larger, null hypothesis is rejected, and there is a difference.
What are degrees of freedom in one-way chi square analyses dependant on?
Number of cells, not number of participants - df = k (or cells) - 1
How is the testing criteria/expected distribution decided when running a one-way chi square analysis? What are the most common expected distributions?
Could be based on actual, plausible expected distribution (already knowing categories won't be equal), or simple equivalency distributions (equiprobable distributions, which are most common)
How do one-way and two-way chi square tests differ?
- Test of goodness of fit v test of independance
- Null hypothesis: two populations are identical v two variables are distributed independantly
- expected frequencies alone v marginal totals as focus
What are some of the assumptions and limitations of chi-square analysis?
Assumptions:
- independance of observations (results can't be dependant on each other)
- expected cell frequencies of at least 5
- inclusion of all non-occurrences (don't exclude any data)
Limitations:
- can only use chi-square analysis with 1 or 2 variables
- DFs are based on number of cells, so sample size has strong influence on chi-square and significance
What is Phi? How is it found?
The measure of association between categorical variables in a 2x2 chi square. Interpret same way as Pearson's correlation.
Can be found by adding 'PHI' to the end of the CHISQ component of the STATISTICS function in SPSS.
How do you found variance accounted for with chi-square analysis?
Square the Phi value found via SPSS
The table displaying observed frequencies in two-way chi square analysis is also known as the...
Contingency table
What is the formula for calculating expected frequencies in two-way chi-square analysis? How many times does this generally need to be done?
fe = (col total x row total)/grand total

Generally, four times, one for each cell.
What is the formula for calculating chi-square in two-way chi square analysis?
= the sum of all ((obtained frequency - expected frequency)^2 / expected frequency)
How do you interpret the chi-square result obtained in two-way analysis to see whether null hypothesis should be rejected?
Using the degrees of freedom calculated, find the appropriate critical chi-square value and compare to the obtained. If obtained > critical, null hypothesis of independence is rejected, and it can be concluded that distributions are dependant on each other.
What version of Phi can be used when tables are larger than 2x2 (that is, variables have more than two conditions)?
Cramer's phi - denoted as Phi symbol c. Interpreted same way.
What implications for statistical analysis lie in the 'independence of observations' assumption of chi-square analysis?
Means you cannot use repeated measures designs, as participants can only fall in one category
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