How to Conduct and Interpret Correlation Tests
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The document provides guidance on conducting and interpreting correlation tests, detailing both parametric and non-parametric techniques, such as Pearson, Point-Biserial, and Spearman correlations, as well as Chi-Square tests. It emphasizes the importance of checking for normality assumptions and suggests alternatives if the data does not meet these requirements. Additionally, it highlights the role of p-values and effect sizes in analyzing correlated data and stresses the need for careful selection of correlation methods based on the level of measurement of variables.
How to Conduct and Interpret Correlation Tests
- 1. How to Conduct and Interpret Correlation Tests Justin D’Souza Quantitative Specialist
- 2. Table of Contents Statistics Solutions Services Selecting a Correlation Analysis SPSS Demo Summary Need help with your dissertation? Call 727-442-4290
- 3. Services Offered by Statistics Solutions • Topic Development • Prospectus or Concept Papers • Introduction Chapter • Literature Review Chapter (identifying articles) • Methodology Chapter (Quantitative/Qualitative). • IRB forms • Data entry templates • Survey Monkey upload • Results Chapter (Quantitative/Qualitative) • Discussion Chapter • Powerpoints for Defense • Journal Publications Need help with your dissertation? Call 727-442-4290
- 4. Parametric and Non-Parametric Statistics Parametric Techniques Parametric statistics are based on assumptions about the distribution of population from which the sample was taken. Usually this “assumption” is that the data follows a normal (bell-shaped) distribution. Usually parametric analyses are used when examining continuous variables. Examples: Pearson correlations, point-biserial correlations Non-Parametric Techniques Nonparametric statistics are not based on strict assumptions, that is, the data can be collected from a sample that does not follow a specific distribution. A normal (bell-shaped) distribution is not required for non-parametric techniques. Examples: Spearman correlations, Kendall’s Tau correlations, Chi-Square test of independence Need help with your dissertation? Call 727-442-4290
- 5. Normality Assumption Typically, parametric statistics assume that the data follow a normal (bell-shaped) distribution. There are various ways to check for normality (Shapiro-Wilk test, Kolmogorov- Smirnov test, skewness/kurtosis, scatterplots/histograms). And if the data do not follow a normal distribution, non-parametric techniques can potentially be used as an alternative. If you have a large sample size (>50), you can use the central limit theorem to justify using parametric techniques even if tests normality are not showing a bell-shaped curve. Howell (2013) states that violations of normality are not problematic when the sample size for research exceeds 50 cases. Howell, D. C. (2013). Fundamental statistics for the behavioral sciences (8th ed.). Belmont CA: Brooks/Cole-Thompson Learning. Need help with your dissertation? Call 727-442-4290
- 6. Level of Measurement Continuous – variables that fall on a continuum. Examples: test scores, temperature, weight, composite scores on a previously validated instrument. Nominal - variables that have two or more categories, but which do not have an intrinsic order. Examples: Gender, ethnicity, pass/fail of an exam. Ordinal - variables that have categories just like nominal variables only the categories can also be ordered or ranked. Examples: education, ordinal item on a survey (strongly agree, agree, neutral, disagree, strongly disagree) Need help with your dissertation? Call 727-442-4290
- 7. Types of Correlations Parametric Techniques- Pearson correlation – Tests the association between two continuous level variables. Point-biserial correlation – Tests the association between a dichotomous (nominal) variable and a continuous variable. Non-parametric Techniques- Spearman correlation – Tests the association between two variables, when at least one variables is measured on an ordinal level. Chi-Square tests of independence – Tests the association between two nominal level variables. Need help with your dissertation? Call 727-442-4290
- 8. Three Statistics to Interpret for Correlations Examine the p-value to identify if a significant relationship exists between the variables (typically p < .05). Identify the sign of the correlation – is it positive (direct) or negative (inverse). Apply Cohen’s standard to interpret the strength of correlation coefficients for Pearson, point-biserial, and Spearman correlations. Cohen’s standard (Cohen, 1988) will be used to evaluate the correlation coefficient to determine the strength of the relationship, where coefficients between .10 and .29 represent a small association; coefficients between .30 and .49 represent a medium association; and coefficients above .50 represent a large associate or relationship. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). St. Paul, MN: West Publishing Company. Need help with your dissertation? Call 727-442-4290
- 9. Pearson Correlation A Pearson correlation is a parametric technique that assesses for the relationship between two continuous variables. Assess for normality first with Shapiro-Wilk tests, Kolmogorov- Smirnov test, skewness/kurtosis, or histograms. If normality is not supported, you may want to consider using a Spearman correlation. If your sample size is large, it is often acceptable to proceed with Pearson correlation even if the normality assumption is not supported. Use the Howell (2012) citation. SPSS: Analyze -> Correlate -> Bivariate Move all variables of interest to the right box Check the “Pearson” correlation box under correlation coefficients. Need help with your dissertation? Call 727-442-4290
- 10. Point-Biserial Correlation A point-biserial correlation is a parametric technique that is used when testing the association between a dichotomous variable and a continuous variable. Due to having a continuous variable, you need to check for normality (similar verification as a Pearson correlation) If normality is not supported, you may want to consider using a Mann-Whitney U test. SPSS: Analyze -> Correlate -> Bivariate Move all variables of interest to the right box Check the “Pearson” correlation box under correlation coefficients. Need help with your dissertation? Call 727-442-4290
- 11. Spearman Correlation A Spearman correlation is a non-parametric technique that assesses for the relationship between two variables, when at least one variable is measured on an ordinal level. There are not strict assumptions to verify for a Spearman correlation because the data is non-parametric. However, if you propose a Pearson correlation, and normality is not supported with a small sample size – you may want to adjust to using a Spearman correlation instead. SPSS: Analyze -> Correlate -> Bivariate Move all variables of interest to the right box Check the “Spearman” correlation box under correlation coefficients. Need help with your dissertation? Call 727-442-4290
- 12. Chi-Square Test of Independence A chi-square test of independence is used when testing the association between two nominal-level variables. SPSS: Analyze -> Descriptives -> Crosstabs Move variable to row and variable to column. Select “Statistics” option, and check the “Chi-square” box. Need help with your dissertation? Call 727-442-4290
- 13. Summary Identify which type of correlation is best for your research question based on level of measurement of variables. Check for assumptions on parametric statistics. Move to a non-parametric statistic if normality is not supported or justify proceeding with a large sample size. Need help with your dissertation? Call 727-442-4290
- 14. Additional Support Statistics Solutions is a full-service dissertation consulting company providing graduate students timely, editorial support for their dissertations and scholarly projects For information about our services, receive a complementary 30-min consultation available Mon-Fri 9-5 ET Contact us at info@statisticssolutions.com Phone: 727-442-4290