week 4. Chi-Square

Question 1

Chi-Square test

Answer 1

Best used for frequency data, as opposed to data scores.Use chi-square Goodness of Fit Test to eg examine whether sample proportion of male and female lawyers different to population. A one way classification is the simplest form of chi square test, and has only 1 variable.

X²=Chi squared=Σ(O-E)²/E

O=observed frequency and E =expected frequency

Question 2

Decision for Chi-squared

Answer 2

If X² _obtained>/= X²_critical then we reject the null hypothesis.

Degrees of freedom =number of categories minus 1.

Usually set alpha as 0.05.

Table then tells us X²_critical

Question 3

2-way classification, use Chi-square Test for Independence

Answer 3

for more complex situations, eg. to see if two variables are independent. eg is lemonade preference dependent upon gender?

Need to construct a contingency table which shows the distribution of one variable, at all levels of the other. For the contingency table, need to calculate all expected frequencies.

E_ij=R_iC_j/N

R=row total, C=Column total, N=total number of observations.

Once have all expected frequencies (E),

then do

Chi²=Σ(O-E)²/E

Degrees of freedom=(R-1)(C-1)

If Chi²_obtained>/=Chi²_critical, then we reject the null hypothesis.

Question 4

effect size

Answer 4

A further measure to quantify how significant, a significant difference (once found), is.

Question 5

d-family

Answer 5

effect sizes which focus on the differences between groups. eg. probability of choosing lemonade B, for male vs female

Question 6

r-family

Answer 6

effect sizes used to determine the magnitude of a relationship between 2 variables.

Question 7

Phi

Answer 7

When using a Chi-square 2x2 table, Phi can be used to determine the magnitude of effect.

phi= square root of (Chi²/N)

By convention, phi=0.10=small effect

phi=0.30=medium effect

and phi=0.50 = large effect

Question 8

Cramer’s V

Answer 8

used for magnitude of effect when have a larger than 2x2 contingency table.

V=square root of [Chi²/(N{k-1})]

where k is the lesser of Number of Rows or Number of Columns.

The magnitude levels of Cramer’s V, are the same as for Phi.