PSYC20009 Chap.3 Correlation, Reliability and APA Results
Correlation, Reliability and APA Results
Quantitative reasoning in the subject requires several outputs to keep separate jobs. Cronbach's alpha addresses internal consistency reliability and does not establish validity. Pearson's correlation coefficient describes the direction and strength of a linear association. Its sign provides direction, its absolute magnitude provides effect size and its p-value addresses statistical significance under a null model.
Degrees of freedom for Pearson's r are calculated as sample size minus two. The laboratory-report guidance also requires relevant descriptive statistics, reliability for the subscales central to the hypotheses, three correlation analyses and at least one table. APA reporting is part of scientific communication, but correct formatting cannot widen a design.
Correlational evidence supports association language unless additional design features justify prediction or causation. This chapter trains accurate calculation, reporting and inference rather than treating software output as a conclusion.
What this chapter covers
- 01
Internal consistency as coherence among scale items
- 02
Cronbach's alpha as reliability evidence rather than validity
- 03
Pearson's r as a linear-association coefficient
- 04
Positive and negative direction from the coefficient sign
- 05
Effect size from the coefficient's absolute magnitude
- 06
Statistical significance from the p-value
- 07
Degrees of freedom calculated as sample size minus two
- 08
Descriptive statistics for relevant scales and participants
- 09
APA formatting for coefficients and exact p-values
- 10
Association language and the limits of causal interpretation
Worked example · free
Report an original correlation output
- 1Degrees of freedom are 64 minus 2, which equals 62.
- 1The negative sign means higher planning is associated with lower distraction.
- 1The absolute value .42 falls in the medium band under the course-taught rule of thumb.
- 1Report r(62) = -.42, p = .002 and retain association language because causation was not established.
Key terms
- Internal consistency
- The degree to which items designed to form one scale behave coherently as indicators of a common idea.
- Cronbach's alpha
- A numerical coefficient used here to summarise internal consistency after items are coded in the same direction.
- Pearson correlation
- A coefficient ranging from negative one to positive one that describes a linear association's direction and strength.
- Effect size
- The magnitude of an observed relationship, which is distinct from whether a significance threshold is crossed.
- Statistical significance
- A judgement based on a p-value under a null model, not a direct measure of practical importance.
- Degrees of freedom
- For Pearson's correlation, the sample size minus two, reported inside parentheses after the coefficient symbol.
- Descriptive statistics
- Summaries such as means, standard deviations, ranges, frequencies and percentages that describe the analysed data.
Correlation, Reliability and APA Results FAQ
Does a high alpha prove validity?
No. A scale can contain items that behave consistently while measuring the wrong construct. Alpha supports internal consistency; construct validity requires separate theoretical and empirical evidence.
How are direction and strength read from r?
The positive or negative sign gives direction. Strength comes from the absolute magnitude, so a coefficient of -.60 is stronger than a coefficient of .20 despite being negative.
Can a small correlation be significant?
Yes. Statistical significance depends partly on sample size and uncertainty, while strength concerns the coefficient's magnitude. The two judgements should always be reported separately in the result.
What belongs in the Results section?
Describe the analysis, present relevant descriptive statistics and report the hypothesis tests with coefficients, degrees of freedom and p-values. Interpret broader meaning and limitations in the Discussion.
Why should tables not be repeated in prose?
Repeating every table value wastes limited report space and makes the result harder to follow. Use prose for hypothesis-relevant patterns and the table for the organised set of values.
Exam move
Create a four-box interpretation routine: direction, strength, significance and design. Work original outputs until you can compute degrees of freedom, select the correct strength band and write an APA-style sentence without looking at a template. Make a contrast card for reliability and validity, using one example of a consistent but invalid measure.
Practise identifying redundant result presentation by comparing paragraphs with tables. When reviewing a correlation claim, replace causal verbs with association language and then ask what design would be needed to restore the causal statement. Finish by checking the laboratory-report requirements for relevant subscales, descriptive summaries, three correlations and at least one appropriately formatted table.
Run a numerical audit on every practice output: for Pearson correlation, calculate df = n - 2, read the ± direction of r before its magnitude and treat the p-value as a separate uncertainty decision. Write Cronbach's α beside the phrase internal consistency so the symbol never becomes a shortcut for validity.
Create paired statements that keep the same coefficient but change sample size, then explain why significance can change while effect size does not. Finally, convert one table row into a complete results sentence and highlight the statistic, degrees of freedom, coefficient and p-value in different colours.
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