1. Analyzing Chi-Squares and Correlations
Dr. K. A. Korb
University of Jos

2. Outline Chi-Square Correlation Purpose Null Hypotheses Interpreting
Reporting
Correlation
Dr. K. A. Korb
University of Jos

3. No Yes Yes No Yes No Yes No No Yes
Dr. K. A. Korb
University of Jos
Do you have categorical data only? No
Yes
Do you have independent and dependent variables?
Chi-Square
(χ2)
Do you have more than 2 groups or independent variables?
Yes No
Do you have more than 2 variables?
Yes
Do you have pre- and post-tests? No
Yes No No
Yes
ANOVA: Analysis of Variance
ANCOVA: Analysis of Covariance
t-test
Regression
Correlation

4. Chi-Square
Dr. K. A. Korb
University of Jos

5. Purpose of Chi-Square
A descriptive research design is to determine the type of instruction that Nigerian children prefer.
The three possible types of instruction include online presentation, lecture, and discussion.
This type of variable is called nominal, or categorical.
Nominal scale is one in which categories have no quantitative value. In other words, categories are just names.
Since we cannot meaningfully assign numbers to the category of variables, we must use a Chi-Square test.
Dr. K. A. Korb
University of Jos

6. Purpose of Chi-Square
The purpose of conducting a Chi-Square analysis is to determine whether frequency counts are equivalently distributed.
Two conditions must be met to conduct a Chi-Square
Each and every data point falls into only one category
The sample size must be large
The Chi-Square statistic compares the actual frequency distribution to an expected frequency distribution.
Dr. K. A. Korb
University of Jos

7. Chi-Square Null Hypotheses
The first step in creating null hypotheses for a Chi-Square is to determine the expected frequency of your data
The expected frequency distribution must be set before collecting your data.
Once you have set your expected frequency, the null hypothesis is that there is no significant difference between the expected and observed frequency distributions.
Dr. K. A. Korb
University of Jos

8. Chi-Square Null Hypotheses
Expected Frequency Distribution for Students’ Instructional Preference
Type of Instruction
Frequency
Online Presentation 50
Lecture
Discussion
There will be 150 students in the sample.
The expected frequency distribution is that equal numbers of students will prefer each type of instruction.
Null hypothesis: There are no significant differences between the frequency of students who prefer each of the three types of instruction.
Dr. K. A. Korb
University of Jos

9. Chi-Square Null Hypotheses
Expected Frequency Distribution for Students’ Instructional Preference
Type of Instruction
Frequency
Online Presentation 50
Lecture
Discussion
Observed Frequency Distribution for Students’ Instructional Preference
Type of Instruction
Frequency
Online Presentation 75
Lecture 10
Discussion 65
The Chi-Square statistic quantifies the discrepancy between the expected and observed frequency charts.
Dr. K. A. Korb
University of Jos

10. Interpreting Chi-Square
When calculating a Chi-Square, there are three important statistics
The χ2 (symbol for Chi-Square)
The χ2 is a function of the amount of discrepancy between the expected and observed data
The degrees of freedom
Degrees of freedom is the number of categories compared minus 1
The example has 3 categories: online presentation, lecture, and discussion
The degrees of freedom is (3 – 1 =) 2
Probability (p): This tells whether the χ2 is large enough for the results to generalize beyond the sample
For Chi-Square statistics, you also must report the size of your sample (N)
Dr. K. A. Korb
University of Jos

11. Interpreting Chi-Square
The p value for a Chi-Square is interpreted exactly the same as for inferential statistics
If the p value is less than .05, the results are considered significant.
The significance level that is set prior to conducting statistics is the alpha (α)
If the calculated p value is less than the alpha, then the null hypothesis is rejected.
Significant p-values indicate that the results are NOT due to chance and thus represent a meaningful difference between the expected and observed frequencies.
It can then be concluded that a difference does exist between the expected and observed frequencies.
Dr. K. A. Korb
University of Jos

12. Reporting Chi-Square
There was a significant difference between the expected and observed frequencies of students’ preference of instruction, indicating that students do have one preferred method of instruction (χ2(2, N = 150) = 10.51, p = .03).
2 is the degrees of freedom
N = 150 is the sample size
10.51 is the χ2 value
p = .03 is the significance
Dr. K. A. Korb
University of Jos

13. Correlation
Dr. K. A. Korb
University of Jos

14. Purpose of Correlations
The purpose of a correlation is to determine the relationship between two naturally occurring variables
The correlation quantifies two aspects of the relationship between variables: the nature and the strength
Dr. K. A. Korb
University of Jos

15. Purpose of Correlations
Correlational research must meet two conditions:
The variables must be naturally occurring (i.e. no treatment or control groups)
Both variables must be continuous in nature (i.e. vary on a continuum from low to high levels with many possible points between)
For example, a typical correlation between motivation and grade for junior secondary students would not be possible because only three grades exist – JS1, JS2, and JS3
However, a correlation between motivation and age would be possible because age represents a continuous variable
Dr. K. A. Korb
University of Jos

16. Purpose of Correlations
A correlational research study examines the relationship between interest in maths and maths performance.
Data is collected by administering a questionnaire to assess interest in maths
The researcher would also collect maths performance data from school records
Dr. K. A. Korb
University of Jos

17. Interpreting Correlations
Correlational research one important statistic
Correlation: Indicates the strength and direction of a relationship
A p value can also be calculated for a correlation
The p value depends on both the magnitude of the correlation and the size of the sample
The p value indicates whether the correlation is significant enough for the results to generalize to beyond the sample
However, the correlation is the most meaningful statistic for correlational research designs.
Dr. K. A. Korb
University of Jos

18. Interpreting Correlations
Correlations range between -1.0 to +1.0
Nature
Positive: Two variables increase or decrease together
Negative: As one variable increases, the other decreases
Strength
Closer to -1 or +1 is stronger relationship
0 is no relationship
Dr. K. A. Korb
University of Jos

19. Interpreting Correlations
Dr. K. A. Korb
University of Jos
Interpreting Correlations
Nature:
Negative
Positive -1 +1
Strength:
Nature
Positive: Two variables increase or decrease together
Negative: As one variable increases, the other decreases
Strength
Closer to -1 or +1 is stronger relationship
0 is no relationship

20. Interpreting Correlations
Dr. K. A. Korb
University of Jos
Interpreting Correlations
Correlation
Nature
Strength
Interpretation
.95
Positive
Strong
The strong correlation indicates that as interest increases, performance also increases.
-.10
Negative
Weak
There is very little relationship between interest and performance.
-.50
Moderate
The moderate correlation indicates that as interest increases, performance tends to decrease.
.05
Very Weak
There is no relationship between interest and performance.
-.75
The strong correlation indicates that as performance increases, interest tends to decrease.

21. Null Hypothesis for Correlations
Since correlations quantify the relationship, null hypotheses for correlations are in terms of the relationship between variables.
There is no significant relationship between maths interest and maths achievement.
Dr. K. A. Korb
University of Jos

22. Reporting Correlations
A correlation of .54 between maths interest and maths performance was found (df = 67, p = .03), indicating that students who are more interested in maths tend to have higher maths performance.
Dr. K. A. Korb
University of Jos

23. Reporting Correlations
This scatter plot graph created in Excel demonstrates that as maths interest increases, so does maths performance, a positive correlation.
Dr. K. A. Korb
University of Jos