Data Interpretation in Statistics for Psychology

Learning Objectives

• Integrate descriptive statistics, inferential statistics, and correlation/regression into a single reading of a research result.
• Critically evaluate a statistical claim by checking context, causation vs. correlation, and study limitations.
• Interpret combined statistics reports (e.g., "M = 83.6, SD = 7.43, t(28) = 2.1, p = .04") the way they appear in journal articles.
• Identify common ways statistics are misrepresented in media coverage of psychological research.
• Apply critical thinking questions to judge whether a psychological claim is adequately supported by its data.

Quick Answer

Data interpretation is the skill of reading statistical results and correctly translating them into psychological meaning — it's where everything from earlier chapters (descriptive statistics, inferential statistics, correlation, and hypothesis testing) comes together. Rather than treating a mean, a p-value, or a correlation coefficient as an isolated number, good data interpretation asks what the numbers actually say about behavior, how confident we should be, and what limitations (sample size, study design, confounds) might change that conclusion. This is arguably the single most exam-relevant and career-relevant skill in the whole statistics unit, since most professional and academic tasks involve reading someone else's results, not calculating your own from scratch.

Reading a Combined Statistics Report

Journal articles rarely give you just one number. Consider this typical sentence from a hypothetical psychology paper:

"Participants in the mindfulness group (M = 18.2, SD = 4.1, n = 30) reported significantly lower anxiety than the control group (M = 23.5, SD = 5.6, n = 30), t(58) = 3.94, p < .001, d = 1.02."

Breaking this down piece by piece is exactly the skill this chapter builds:

• M and SD (descriptive statistics): the mindfulness group averaged 18.2 with moderate spread (SD 4.1); the control group averaged 23.5 with more spread (SD 5.6).
• t(58) = 3.94: an independent-samples t-test statistic, with 58 degrees of freedom (df = n1 + n2 − 2 = 30+30−2).
• p < .001: the probability of seeing a difference this large if there were truly no effect is extremely small — strong evidence against H0.
• d = 1.02: Cohen's d, an effect size measure; d = 1.02 is considered a very large effect (by convention, 0.2 = small, 0.5 = medium, 0.8+ = large), meaning the difference isn't just statistically significant but also practically substantial.

Notice how each number answers a different question: "what happened" (M, SD), "is it likely real" (t, p), and "does it matter" (d). Skilled data interpretation reads all three together — a common exam and real-world failure is fixating on the p-value alone.

Worked Example: Full Descriptive Walkthrough

Exam scores from a psychology class: 78, 85, 90, 75, 95

Mean = (78+85+90+75+95)/5 = 423/5 = 84.6 Ordered: 75, 78, 85, 90, 95 → Median = 85 Mode: none (all values unique)

Deviations from the mean (84.6): −6.6, 0.4, 5.4, −9.6, 10.4 Squared deviations: 43.56, 0.16, 29.16, 92.16, 108.16 Sum = 273.2; Variance (sample, n−1=4) = 273.2/4 = 68.3 Standard deviation = √68.3 ≈ 8.26

Interpretation, not just calculation: the mean (84.6) and median (85) are close, suggesting a roughly symmetric distribution. An SD of about 8.26 on a 100-point exam indicates moderate spread — most students scored within roughly 8 points of the average, neither an unusually consistent nor unusually scattered class.

The Critical-Thinking Layer

Numbers alone don't interpret themselves. Three questions should accompany every statistic you read:

1. Context: What was the research question? What population was sampled? A finding about university students may not generalize to older adults or clinical populations.
2. Causation vs. correlation: Does the study design (experimental vs. correlational) actually support a causal claim, or only an associative one?
3. Limitations: What was the sample size? Was there selection bias? Could a confound explain the result better than the proposed explanation?

Real-World Application

Health journalism is full of data interpretation failures worth learning to spot. A headline like "New Study: Coffee Drinkers Live Longer" is often based on a correlational study; a careful reader checks whether the study controlled for confounds (income, smoking, exercise), whether the effect size was meaningful or tiny, and whether "significant" meant statistically significant or practically significant. Psychology students who master data interpretation are far better equipped to evaluate not just academic research, but every "studies show" claim in the news and on social media.

Key Terms

Term	Definition
Effect size	A standardized measure of the magnitude of a finding (e.g., Cohen's d, r), independent of sample size
Cohen's d	A common effect size measure for the standardized difference between two means
Statistical significance	A result unlikely to occur by chance under the null hypothesis (p < α)
Practical significance	Whether a finding is large enough to matter in real-world terms
Degrees of freedom (df)	The number of values free to vary in a calculation, used to determine critical values for a test
Selection bias	A systematic error in how a sample was chosen, threatening how well it represents the population
Confound	An uncontrolled variable that offers an alternative explanation for a result

Common Mistakes

1. Misconception: "If a result is statistically significant, it must be an important, large effect." Why it's wrong: Statistical significance depends heavily on sample size; large samples can make even trivially small effects statistically significant. Correct: Always pair a significance test with an effect size (like Cohen's d or r) to judge the practical magnitude of a finding.

2. Misconception: "A correlational study showing X and Y are related is basically as good as an experiment for establishing causation." Why it's wrong: Correlational designs cannot rule out reverse causation or confounding variables, no matter how strong the correlation. Correct: Only well-controlled experiments with random assignment and manipulation of the independent variable can support causal claims; correlational studies support associative claims only.

3. Misconception: "A non-significant result (p > .05) means there is definitely no effect." Why it's wrong: A non-significant result could reflect a genuinely null effect, or it could reflect an underpowered study (too small a sample to detect a real, smaller effect). Correct: Interpret a non-significant result cautiously, considering the study's sample size and power before concluding "no effect exists."

Comparison and Connections

Question you're asking	Statistic to check
"What did the data look like?"	Mean, median, mode, SD (descriptive)
"Is the difference/relationship likely real?"	p-value, t/F/χ² statistic, confidence interval (inferential)
"How big or important is the effect?"	Effect size (Cohen's d, r, r²)
"Can I conclude X causes Y?"	Study design (experimental vs. correlational), not the statistic itself
"Can I trust this generalizes beyond the sample?"	Sample size, sampling method, replication across studies

Practice Questions

Recall

1. List the three broad categories of statistics that combine to form a complete interpretation of a research result. Answer guidance: Descriptive statistics (what the data show), inferential statistics (is it likely real), and effect size/design considerations (does it matter and can it support causal claims).
2. Define effect size and name one common measure of it. Answer guidance: Effect size is a standardized measure of how large a finding is, independent of sample size; Cohen's d is a common example.

Understanding 3. Explain why a very large sample size can produce statistically significant results even for a trivially small effect. Answer guidance: Larger samples reduce standard error, making even small differences detectable at conventional significance thresholds; significance reflects reliability of detecting a difference, not its size. 4. Why should a reader check study design (experimental vs. correlational) before accepting a causal claim in a news article? Answer guidance: Only experimental designs with random assignment and manipulation can rule out reverse causation and most confounds; correlational designs, however strong the association, cannot establish causation alone.

Application 5. A study reports "M = 55, SD = 12" for a stress scale in one group and "M = 42, SD = 10" in another, with t(48) = 4.2, p < .001, d = 1.15. Interpret this result in plain language. Answer guidance: The first group scored notably higher on stress than the second group (55 vs. 42); this difference is very unlikely to be due to chance (p < .001) and represents a large, practically meaningful effect (d = 1.15), not just a statistically detectable one. 6. A news article states "Study finds people who meditate are happier" based on a survey correlating meditation frequency with happiness scores. What follow-up questions should a critical reader ask before accepting this as evidence that meditation causes happiness? Answer guidance: Was this an experimental or correlational design? Could happier people simply be more likely to take up meditation (reverse causation)? Were confounds like income, social support, or health controlled for? What was the effect size, not just significance?

Analysis 7. Two studies test the same hypothesis: Study A (n = 20) finds p = .08; Study B (n = 200) finds p = .03, with a similar effect size in both. Analyze what this pattern likely reflects about statistical power. Answer guidance: Study A was likely underpowered to detect the effect reliably given its small sample, producing a non-significant result despite a real effect being present; Study B's larger sample gave it more power to detect essentially the same-sized effect as statistically significant, illustrating why sample size affects significance independent of true effect size. 8. Critically evaluate the claim: "The correlation between screen time and reported loneliness was r = .35 (p < .01), proving that screen time causes loneliness." Answer guidance: The correlation is statistically significant and moderate in strength, but "proving causation" overstates what a correlational finding can establish; reverse causation (lonelier people using screens more) or confounds (e.g., social anxiety) remain plausible alternative explanations that only an experimental design could rule out.

FAQ

Why is data interpretation considered harder than calculating statistics? Calculation follows fixed formulas, but interpretation requires judgment — weighing sample size, design, effect size, and context together, which has no single "correct" formula and depends on critical thinking.

What's the difference between statistical significance and practical significance? Statistical significance tells you a result is unlikely to be due to chance; practical significance tells you whether the effect is large enough to matter in real life. A result can be statistically significant but practically trivial, or vice versa in underpowered studies.

How much should I trust a single study's results? Be cautious — a single study, however well-designed, can be affected by chance, sampling limitations, or unmeasured confounds. Replication across multiple studies (and meta-analyses combining many studies) provides much stronger evidence.

What red flags should I look for in a research claim reported in the media? Watch for causal language ("causes," "proves") applied to correlational data, missing information about sample size or effect size, cherry-picked single studies, and a lack of comparison to a control group.

Is it possible for a result to be both statistically significant and misleading? Yes — for example, with a very large sample, a tiny and practically meaningless difference can reach statistical significance, or a significant correlation can be misinterpreted as proof of causation. Significance alone never guarantees a claim is meaningful or correctly interpreted.

Quick Revision

• Data interpretation combines descriptive statistics (what happened), inferential statistics (is it likely real), and effect size (does it matter).
• A full results report like "M = 18.2, SD = 4.1, t(58) = 3.94, p < .001, d = 1.02" answers three separate questions — always unpack each part.
• Cohen's d benchmarks: ~0.2 small, ~0.5 medium, ~0.8+ large effect.
• Statistical significance depends on sample size; it does not automatically mean a large or important effect.
• Correlational designs support associative claims only; only controlled experiments support causal claims.
• Non-significant results may reflect a true null effect or simply an underpowered study — don't assume "no effect" automatically.
• Always ask about context, causation vs. correlation, and limitations before accepting a statistical claim.
• Replication across multiple studies is far stronger evidence than any single study, however well-designed.
• Media coverage of psychological findings often overstates causal claims from correlational data — read critically.

Related Topics

Prerequisites: Descriptive Statistics, Inferential Statistics, Hypothesis Testing, Correlation and Regression.

Related: Research Methods in Psychology, Critical Thinking in Psychology.

Next: Applying these skills directly to reading and evaluating published psychological research studies.