Download - Chi Square Tests (Part 1)
(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