week 12: chi-square tests

Question 1

non-parametric tests

Answer 1

non-parametric tests (hypothesis-testing procedures making no assumptions about population parameters)
eg. iv and dv are nominal

Question 2

Determining Expected Frequencies

Answer 2

expected frequency= expected percentage x N

Question 3

Chi-square (c2) test for goodness of fit

Answer 3

do the observed frequencies of observations in categories fit the expected frequencies?
does the observed distribution fit the expected distribution?

Question 4

Expected and observed frequencies for degree of mismatch

Answer 4

use the Expected (E) and Observed (O) frequencies to calculate the degree of mismatch (the opposite of fit)
use sigma

Question 5

steps for calculating the chi-square statistic

Answer 5

1. Find the actual, observed frequencies in each category
2. Determine the expected frequencies in each category
3. In each category, compute observed minus expected frequencies
4. Square these differences in each category
5. Divide each squared difference by the expected frequency for its category
6. Add up the results of previous step for all the categories

Question 6

Calculating the x2 statistic

Answer 6

calculate the difference between O and E
O-E
square this value to remove any negative signs
(O-E)2
divide by the Expected frequency to remove the effect of the size of expected frequencies
(O-E)2/E
add across all categories
SIGMA(O-E)2/E

Question 7

chi distribution (df)

Answer 7

df = no. categories -1(for goodness of fit)

positively skewed

Question 8

expected frequency calculation

Answer 8

expected frequency=expected percentage x N

Question 9

if the calculated chi square is less than the critical chi-square what does it mean?

Answer 9

that you retain null hypothesis (H0)

Question 10

Chi-square (c2) test for independence

Answer 10

more common in research to have >1 variable
two nominal variables each with multiple categories
chi-square (c2) test for independence
is there a relationship between the way observations are distributed across one variable and the way they are distributed across the other variable?
are they independent? (i.e., no relationship between the variables)

Question 11

Calculating the expected frequencies

Answer 11

contingency table
for each cell, calculate the expected frequency
Econtingency= (R*C)/N
R = Row total
C = Column total
N = Grand total

Question 12

Calculating the expected frequencies for Chi-square (c2) test for independence

Answer 12

contingency table
for each cell, calculate the expected frequency
Econtingency= (R*C)/N
R = Row total
C = Column total
N = Grand total

Question 13

df Chi-square (c2) test for independence

Answer 13

fd= (columns-1)x(rows-1)

• df is the number you use to look up the critical cut off.
  eg. 1df with 0.05 is 3.841 on chi table

Question 14

if chi square is greater than critical chi-square?

Answer 14

Reject H0 (null)

Question 15

Effect size in c2 tests (strength of relationship in c2 tests of independence)

Answer 15

O with vertical line: phi = strength of the relationship in 2 x 2 Chi-square (x2) tests
- display as percentage