Wk 10 - Chi-square

Question 1

What tests would you use for a one-group research design with…
Nominal data
Ordinal data
Interval/ratio data?

Answer 1

chi-square goodness of fit
Isn’t one
z- or t-test

Question 2

What tests would you use for a two independent groups research design with…
Nominal data
Ordinal data
Interval/ratio data?

Answer 2

chi-square test of independence
Wilcoxon’s rank-sum test
Independent group t-test

Question 3

What tests would you use for a two dependent groups research design with…
Nominal data
Ordinal data
Interval/ratio data?

Answer 3

Isn’t one
Wilcoxon’s matched-pairs test
RM t-test

Question 4

What tests would you use for a three or more independent groups research design with…
Nominal data
Ordinal data
Interval/ratio data?

Answer 4

chi-square test of independence
Kruskal-Wallis one-way ANOVA
One-way independent groups ANOVA

Question 5

What tests would you use for a three dependent groups research design with…
Nominal data
Ordinal data
Interval/ratio data?

Answer 5

Isn’t one
Friedman’s rank test
One-way RM ANOVA

Question 6

How does the Wilcoxon’s matched-pairs signed ranks test differ from the Wilcoxon’s rank sum test? (x2)

Answer 6

It’s for RM not independent groups

So need to calculate difference scores before ranking these

Question 7

What is the difference between a chi-square goodness of fit and test of independence/contingency?

Answer 7

Goodnes asks if the data fits the model - how good does the observed fit with the expected?
Ind/contingency asks if two factors/variables are related - the model is now that two variables are independent

Question 8

How does Sign test relate to the Wilcoxon’s matched pairs ranked sign test? (x2)
And when would we use it instead? (x1)

Answer 8

They are both non-para tests equivalent to dependent groups tests,
But no ranking in Sign tests - just compare how many of each sign there are
When we are not given the raw data, just numbers of eg improved/didn’t

Question 9

How is the chi-square test like the z-test, t-test and ANOVA? (x1)

Answer 9

They all compare expected differences to observed

Question 10

What is the Wilcoxon’s matched pairs signed-ranks test the non-para equivalent of? (x1)
Steps to calculate (x5)

Answer 10

RM t-test
Calculate the diff scores – disregarding any that = 0
Rank the diff scores low to high, ignoring sign – use absolute value of difference
Re-attach the signs (= ‘signed ranks’)
Add positive and negative signs separately
Evaluate smallest absolute value against critical/Wilcoxon’s T: where N = the number of nonzero diff scores; is a one-tailed test table, so divide alpha/2 = .025; use the smaller critical value to be more conservative/make rejection of null harder

Question 11

What is the Kruskal-Wallis one way ANOVA (H-test) the non-para equivalent of?

Answer 11

One way independent groups ANOVA

So, for when you have more than 2 treatment groups

Question 12

What is the Friedman’s rank test for k correlated samples the non-para equivalent of?

Answer 12

One way RM ANOVA

So, for when you have more than 2 treatment groups

Question 13

When do we use the chi-square goodness of fit test? (x2)

Answer 13

When we have qualitative, categorical data

When you have one variable - does it fit the model

Question 14

What is the chi-square goodness of fit the non-para equivalent of? (x1)
What are the steps for calculating? (x3)

Answer 14

No parametric equivalent
Calculate E
Calculate chi-square
Compare with critical chi-square: alpha is for 2-tailed test despite one-tailed comparison distribution, so use .05, df = k – 1

Question 15

What is the logic/null hypothesis of chi-square tests? (x3)

Answer 15

chi-square will be small if diff between observed and expected frequencies are
So is the distance from zero just due to chance?
So null is that chi-square = 0

Question 16

Why do we need to report N for chi-square obtained? (x3)

Answer 16

Because chi-square is a family of distributions, dependent on df
But df is dependent on number of cells (k - 1) not Ps, and
chi-square will be larger for larger samples (doubling N will double it) while critical value stays the same

Question 17

What are 4 ways we could establish expected frequencies for chi-square goodness of fit?
And how do we calculate them?

Answer 17

Uniformly distributed – equiprobable dist
Dist according to established theory, eg proportions of personality type
Dist according to previous observed frequencies, eg last election voting pattern
Normally distributed
Find the percentages and apply them to N

Question 18

When do we use the chi-square test of independence/contingency? (x2)

Answer 18

When there is qualitative, categorical data

When there are 2 variables

Question 19

What is the chi-square test of independence/contingency the non-para equivalent of? (x1)
Steps for calculating?

Answer 19

Fill in contingency table, including totals across rows/columns and grand total – represents the frequencies of joint occurrences
Calculate expected frequencies: row total times column total divided by N
Same chi=square formula as goodness of fit
Df = (number of rows – 1) x (number of columns – 1)
Compare obtained with critical value at .05

Question 20

What is the Sign test the non-para equivalent of? (x1)

Steps for calculation?

Answer 20

RM t-test
H0: + and - differences are equiprobable, so E = N/2
Calculate difference scores – ignore values of differences between scores (eg before/after treatment/exposure), and just use the positive/negative sign (disregard any 0 differences)
N = the number of non-zero differences
Apply chi-square formula
Df = 1, compare to critical chi value, make decision

Question 21

What are the assumptions of chi-square? (x3)

Answer 21

Independence of observations: subject can only be counted in one category - can’t use it for RM, except as sign test (each Ps one sign or other)
E must = at least 5: small E produces few possible chi-square obtained, but we then compare to continuous distribution
Inclusion of non-occurrences: computations must be based on all subjects in the sample, eg can’t just count the girls that pass a test, and compare to number of boys who do – need to use total N, those who pass + those who fail

Question 22

What is Cramer’s phi? (x1)

And when is it used? (x1)

Answer 22

A measure of association between 2 variables

Follow-up for chi-square test of independence

Question 23

How is Cramer’s phi calculated?

Answer 23

Divide chi-square by N(k - 1)
(where k = the smaller of the number of rows or columns)
Then take the root of this

Question 24

What is the difference between Wilcoxons and all other tests of significance? (X1)

Answer 24

The null is rejected if the obtained value is smaller than the critical, rather than larger