(Non-Parametric Techniques) Chi-Square Test ( ) (PART 1)(DR SEE KIN HAI)

1. Use to determine if 2 or more samples differ significantly from each other.2. Use cross-tabulation or contingency tables for 2 nominal category variables. (see L26)3. Analyses only frequencies not percentage.4. If the expected frequencies are too low use Fisher Exact Test.5. There are 2 types of tests

(i) Chi-Square Test for Goodness of Fit : use to analyze single categorical variable to assess the relationship between your data and the predicted data

(a) Equal expected frequencies,(b) Unequal expected frequencies.

(ii) Chi-Square Test for Independence / Relatedness : use to analyze the relationship between 2 categorical variables.

Assumptions to address before you can conduct chi-square tests

1. Data is randomly collected from the population.2. Independence of sample – each data is generated by a different subject.3. If the number of cells < 10, the lowest expected frequency is 5 and observed frequencies can be

any value 0.

Chi-Square Test for Goodness of Fit (Practice)

1

Data ViewVariable View

The Table shows the attitude of 60 students towards PE in SMJA. You are to determine if there is a significant difference in students’ attitude towards PE.

Note: You must tell SPSS 20 to count the [frequency] and not the [scores] so use [Weight Cases].

1. Click on [Data] on the menu bar then [Weight Cases..] to open the dialogue box2. Select [Weight Cases by…] then move [Frequency] into [Frequency Variable] box.

Then [OK] then [Weight On] should appear on the [Status bar] at the bottom.

(a) Equal Expected Frequencies

Null Hypothesis: Assuming that all expected frequencies are equal for each category.

1. Select [Analyze] then [Non parametric Tests] then [Legacy Dialogs] to select [Chi-Square…] to open the dialogue box.

2. Move [Attitude] into the [Test Variable List] then click [OK]

2

PE

Interpreting the output for one sample chi-square (with equal expected frequencies)

3

With equal expected frequencies 1/3 of 60 = 20 each for each category of attitude. So 1=20, 2=20, 3=20

PE

PE

Towards PE Equal expected frequency of 60 =

= 20 for each category

1. First Table shows the [observed], [expected] and the [residual] frequencies row.2. The first column shows the 3 categories of attitude [in favor], [against] and [undecided]. The

second column shows the [observed] frequencies. The third column with equal [expected] frequencies. The last column [residual] = [observed] – [expected] frequencies.

3. The [Test Statistics] table shows that the value of chi-square = 14.4 with degrees of freedom =2 and significance level p = 0.001. As p < 0.05, the observed frequencies differ significantly from the expected frequencies by chance.

Reporting the output for a one sample chi-square

There was a statistical significant difference between the observed and expected frequency for the three categories of attitude towards PE in SMJA students ( = 14.4, DF = 2, p = 0.001).

(b) Unequal expected frequencies (Use the weighted cases as (a)) (We assumed expected frequency for the 3 categories as 1=15, 2=15, 3=30)

1. Select [Analyze] then [Non parametric Tests] then [Legacy Dialogs] to select [Chi-Square…] to open the dialogue box.

2. Move [Attitude] into the [Test Variable List] box.

4

Enter 15 then click [Add] , then 15 [Add] again 30[Add] then [OK]

PE

Interpreting thee output for a one sample chi-square

Reporting the output for a one sample chi-square

There was no statistical difference between the observed and expected frequency for the 3 categories of attitude of students towards PE ( = 5.067, DF =2, p = 0.079).

COURSEWORK (Test of Goodness of Fit) use Equal and unequal N

A Geography teacher wanted to know if there is a significant difference in Year 10 students’ attitude towards geography in his class. He administered a questionnaire to gauge students’ attitude towards geography. Based on students’ responses, Year 10 students’ attitude towards geography has been categorized into:

1 = Positive attitude, 2= Negative attitude and 3 = Uncertain.

The table below shows the frequency distribution of Year 10 students’ attitude towards geography.

Attitude towards Geography Frequency

Positive (1) 7Negative (2) 21Uncertain (3) 32

Total 60

5

PE

This column shows the 3 categories of attitude

Observed frequency (N) – Expected frequency N

The value of = 5.067 and p = 0.079 which is > 0.05 we conclude that the observed frequencies do not differ significantly from those expected by chance