Reporting a correlation

• INTRODUCTION

  In Unit 6, we will apply our understanding of correlation in the third IBM SPSS assignment. For the remaining data analysis assignments (in Units 6, 8, and 10) and for the journal article summary assignment (in Unit 9), we will use the Data Analysis and Application (DAA) Template. The DAA Template is separated into five sections in which you will report the results of your statistical testing.TOGGLE DRAWERHIDE FULL INTRODUCTION

  Proper Reporting of Correlations

  Reporting a correlation in proper APA style requires an understanding of the following elements: the statistical notation for a Pearson’s correlation ( r), the degrees of freedom, the correlation coefficient, the probability value, and the effect size. Consider the following example from Warner (2013, pp. 309–310):

  Only the correlation between commitment and length of relationship was statistically significant, r(116) = +.20, p < .05 (two-tailed). The r² was .04; thus, only about 4% of the variance in commitment scores could be predicted from the length of the relationship; this is a weak positive relationship.

  r, Degrees of Freedom, and Correlation Coefficient

  The statistical notation for Pearson’s correlation is r, and following it is the degrees of freedom for this statistical test (116). The degrees of freedom for Pearson’s r is N − 2. There were 118 participants in the sample cited above (118 − 2 = 116). Note that SPSS output for Pearson’s r provides N, so you must subtract 2 from N to correctly report degrees of freedom. Next is the actual correlation coefficient including the sign. After the correlation coefficient is the probability value ( p).

  Probability Values

  Prior to the widespread use of SPSS and other statistical software programs, p values were often calculated by hand. The convention in reporting p values was to simply state, p < .05 to reject the null hypothesis and p > .05 to not reject the null hypothesis. However, SPSS provides an exact probability value that should be reported instead.Hypothetical examples would be p = .02 to reject the null hypothesis and p = .54 to not reject the null hypothesis (round exact p values to two decimal places). One confusing point of SPSS output is that highly significant p values are reported as .000, because SPSS only reports probability values out to three decimal places. Remember that there is a “1” out there somewhere, such as p = .000001, as there is always some small chance that the null hypothesis is true. When SPSS reports a p value of .000, report p < .001 and reject the null hypothesis.The “(two-tailed)” notation after the p value indicates that the researcher was testing a non-directional alternative hypothesis ( H₁: r_XY ≠ 0). He or she did not have any a priori justification to test a directional hypothesis of the relationship between commitment and length of the relationship. In terms of alpha level, the region of rejection was therefore 2.5% on the left side of the distribution and 2.5% on the right side of the distribution (2.5% + 2.5% = 5%, or alpha level of .05).A “(one-tailed)” notation indicates a directional alternative hypothesis. In this case, all 5% of the region of rejection is established on either the left (negative) side ( H₁: r_XY < 0) or the right (positive) side ( H₁: r_XY > 0) of the distribution. A directional hypothesis must be justified prior to examining the results. In this course, we will always specify a two-tailed (non-directional) test, which is more conservative relative to a one-tailed test. The advantage is that a non-directional test detects relationships or differences on either side of the distribution, which is recommended in exploratory research.

  Effect Size

  Effect sizes provide additional context for the strength of the relationship in correlation. Effect sizes are important because any non-zero correlation will be statistically significant if the sample size is large enough. After the probability value is stated, provide the r² effect size and interpret it as small, medium, or large. It is good form to report the effect size for both significant and non-significant statistics for meta-analyses (that is, statistical studies that combine the results across multiple independent research studies), but in journal articles where space is limited, authors will often report effect sizes only for statistics that reject the null hypothesis.The Warner text provides a “Results” example at the end of each chapter for all statistics studied in this course. You are encouraged to review these examples and follow their structure when writing up Section 4, “Interpretation,” of the DAA Template.

  Reference

  Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: Sage.

Correlations

Resources

•  Correlations Scoring Guide.
•  DAA Template.
•  SPSS Data Analysis Report Guidelines.
•  IBM SPSS Step-by-Step Guide: Correlations.
•  Copy/Export Output Instructions.
•  APA Style and Format.

See the Resources area for links to resources that you will use for this assignment:

1. You will complete this assignment using the Data Analysis and Application (DAA) Template.
2. Read the SPSS Data Analysis Report Guidelines for a more complete understanding of the DAA Template and how to format and organize your assignment.
3. Refer to IBM SPSS Step-By-Step Guide: Correlations for additional information on using SPSS for this assignment.
4. If necessary, review the Copy/Export Output Instructions to refresh your memory on how to perform these tasks. As with your previous two assignments, your submission should be in narrative format with supporting statistical output (table and graphs) integrated into the narrative in the appropriate places (not all at the end of the document).

You will analyze the following variables in the grades.sav data set:

• gender
• gpa
• total
• final

Step 1: Write Section 1 of the DAA.

• Provide the context of the grades.sav data set.
• Include a definition of the specified variables and corresponding scales of measurement.
• Indicate the type of correlation for each X, Y pair (Pearson’s r, Spearman’s r, point-biserial r, et cetera).
• Specify the sample size of the data set.

Step 2: Write Section 2 of the DAA.

• Test the assumptions of correlation for gpa and final.
• Paste the SPSS histogram output for each variable and discuss your visual interpretations.
• Paste SPSS descriptives output showing skewness and kurtosis values and interpret them.
• Paste SPSS scatter plot output with “gpa” set to the horizontal axis and “final” set to the vertical axis. Conduct a visual inspection of the scatter plot to analyze other assumptions of correlation.
• Summarize whether or not the assumptions of correlation are met.

Step 3: Write Section 3 of the DAA.

• Specify a research question related to gpa and final.
• Articulate the null hypothesis and alternative hypothesis.
• Specify your alpha level.

Step 4: Write Section 4 of the DAA.

• Paste the SPSS output of the intercorrelation matrix for all specified variables.
  • First, report the lowest magnitude correlation in the intercorrelation matrix, including degrees of freedom, correlation coefficient, p value, and effect size. Interpret the effect size. Specify whether or not to reject the null hypothesis for this correlation.
  • Second, report the highest magnitude correlation in the intercorrelation matrix, including degrees of freedom, correlation coefficient, p value, and effect size. Interpret the effect size. Specify whether or not to reject the null hypothesis for this correlation.
  • Third, report the correlation between gpa and final, including degrees of freedom, correlation coefficient, p value, and effect size. Interpret the effect size. Analyze the correlation in terms of the null hypothesis.

Step 5: Write Section 5 of the DAA.

• Discuss the implications of this correlation as it relates to the research question.
• Conclude with an analysis of the strengths and limitations of correlational analysis.

Submit your DAA Template as an attached Word document in the assignment area.