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

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

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

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

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

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

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

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

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

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

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

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

Correlation Dr. K. A. Korb University of Jos

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

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

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

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

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

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

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.

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

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

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