Chi Square

Question 1

Tests involving several population Proportions
Test Statistic: Chi-Square (ᵪ^2)
Note: Chi-square test is a test ______?

Answer 1

involving several population proportions or a test of independence of data

Question 2

Uses

Answer 2

To test for relationship between variables that are measured on the categorical scale
To test for independence of data
To test for goodness of fit

Question 3

Conditions of the Chi-Square Test?

One-Way Chi-square
Hypotheses
H_0: There is no relationship between the variables
H_1: There is a relationship between the variables
OR
H_0: Variables are independent
H_1: Variables are not independent

Answer 3

Each observations or frequency must be independent of all other observations
The sample size must be reasonably large in order to ensure that the difference between the actual and expected observations is normally distributed. A sample size of at least fifty (≥ 50) is recommended
Expected frequencies or observations should not be small. In this respect it is recommended that expected frequencies must not less than five (≥ 5) If they are small, merge adjoining cells until they are at least 5
If the degree of freedom equals 1, we apply Yates correction for continuity. i.e., subtract 0.5 from the difference between observed and expected frequencies before squaring
Types:
One-way Chi-square
Two-way Chi-square
Steps
Formulate the hypotheses (Null and alternative)
Specify the level of significance
Indicate the test statistic
Specify the rejection criterion
Compute the Chi-square value
Present the results
Make decision
Implication
Computation of Chi-square (ᵪ^2)
Compute expected frequencies for each cell (f_e)
Find the difference between the observed frequencies (f_o )and expected frequencies (f_e)
Square the deviations in (ii)
Divide the squared deviations by the corresponding expected frequencies
Sum the results in (iv)

Question 4

Formula for chi square

Answer 4

(fO-fe)^2
£. ———
fe

Question 5

What does the table look like

Answer 5

f0 fe fo-fe (fo-fe)^2. fO-fe)^2
———
fE

Fe = mean

Question 6

2-Way Chi-Square
Here, the computation of expected frequencies is not the mean of the observations as done in One-Way Chi-Square

It is computed as:

Answer 6

f_ij = (Ti . x T.J)/(T . .)
Where
f_ij = expected frequency in the ijth cell (i.e. ith row and jth column)
Ti. = sum of the elements in the ith row
T. j = sum of the elements in the jth column

〖ᵪ^2〗calculated = ∑▒(〖f(0 -) f〗_e )^2/f_e

Question 7

What does the table look like

Answer 7

fo
Fe
(Fo-fe)^2