Psychology as a Science: Concepts, Research and Ethics · Lesson 3

Study Design: Correlation, Causation and Reading Data

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Lesson objectives

Choose a descriptive, correlational or experimental design to suit the question.
Identify independent, dependent and confounding variables, and distinguish sampling from random assignment.
Calculate a mean and median and interpret the effect of a distant value and the direction of a relationship from supplied data.
State a conclusion appropriate to the study and propose a comparison that reduces an alternative explanation.

You have a fictional record showing fewer errors among people who practiced longer. Does this mean that extra practice caused the difference? Perhaps, but more experienced people may choose to practice, or they may receive easier tasks. The data can describe a relationship without distinguishing these possibilities. Start not with “Is the number large?”, but with “How were the data obtained, and what comparison was made?”

Three purposes of a study

Purpose	Example question	What can the data support?
Descriptive	How often did participants request instructions again in a specified session?	Description of counts or patterns in that sample and period, not an explanation of cause by itself.
Correlational	Is practice time associated with errors across participants?	A relationship between measured variables, without establishing causal direction.
Experimental	Does performance differ when participants are randomly assigned to two instruction formats?	Comparison of a specified change while controlling other differences; inference depends on implementation and data quality.

These purposes are not a ladder that makes description worthless. Observation or reports may fit questions about experience or events that cannot ethically be changed. Data collection is also distinct from design: an experiment can use self-reports, while an existing record can support a correlational study. Many survey responses do not by themselves establish a cause, and having two groups does not by itself make a study experimental.

First read the numbers in front of you

The arithmetic mean is the sum of the values divided by their count. The median is the middle value after sorting; with an even count, average the two middle values. Both summarize the center but do not describe all the variation. A very long time can pull the mean upward, whereas the median is less affected because it depends on the positions of the values. Choose a summary to fit the question; distant values are not automatically errors to delete.

Fictional case label	Task completion time in minutes
A
B
C
D
E

Association describes a direction, not a cause

A variable is a characteristic or quantity that can differ, such as practice time or error count. In a positive association, higher values of one tend to accompany higher values of the other; in a negative association, they tend to accompany lower values. Positive and negative do not mean good and bad. A pattern may also be curved rather than clearly linear, so no linear association does not mean no possible relationship. A group relationship also does not guarantee prediction for every individual.

What changes in an experiment, and who enters it?

In an experiment, the independent variable is what the researcher deliberately changes between conditions; the dependent variable is the measured outcome. Our next example compares instructions presented as one paragraph or as separate steps: that is the independent variable. The number of steps correctly ordered out of six is the dependent variable. Keep task content, working time and scoring as consistent as possible. Giving one group an easier task as well would prevent attributing the difference to formatting alone.

Sampling determines who enters the study from the group we want to understand, called the study population. Random sampling uses chance to select people from a defined set available for selection, such as a club membership list; this set is the sampling frame. It can help represent the population when the list and procedures are suitable. Random assignment, by contrast, determines which condition each participant receives after entry. It helps reduce systematic group differences but does not guarantee matching on every characteristic, especially in small groups. Random assignment does not turn volunteers from one setting into a sample representing everyone.

Example

Worked design: Twenty volunteers from one learning club consent to a nonsensitive activity. Ten are randomly assigned paragraph instructions and ten separate-step instructions. Everyone receives the same content, six steps to order and the same time; responses are scored by the same rule without showing the scorer the instruction format. Suppose the means are 4 correctly ordered steps for the paragraph and 5 for separate steps. The descriptive difference is 5 − 4 = one correctly ordered step. Assignment and task controls strengthen an interpretation about formatting compared with participants choosing groups, but the two means alone do not show uncertainty or how a new study might differ. Report the difference in these data rather than guaranteed superiority for every learner or topic.

Exercise

Exercise 1 — Fictional task-start times are 1, 2, 4, 5 and 18 minutes. Calculate the mean and median and state what each summarizes. Then suppose the original record establishes that 18 was an entry error and the correct time was 8 minutes. Recalculate both. Would a high value justify deleting it before verification?

Check your answer

Guided solution: Before correction, the sum is 30 minutes; the mean is 30 ÷ 5 = 6 minutes and the median is the third value, 4 minutes. The mean uses every value; the median identifies the middle position, so 6 minutes need not be most participants’ time. After correction the values are 1, 2, 4, 5 and 8; their sum is 20, the mean is 4 minutes and the median remains 4 minutes. The mean changed while the middle position did not. Correction was based on the original record, not discomfort with a value. Had 18 been verified, it would remain in the description while its context was examined.

Exercise

Exercise 2 — In a fictional case, experienced participants choose a brief explanation and beginners choose a longer explanation. The first group scores higher, prompting the claim, “Brevity causes better understanding for everyone.” Identify the proposed independent variable, the measured outcome and the confound. Write a more accurate conclusion and a better comparison plan. Also explain whether random assignment of volunteers within one club alone permits generalization to all adults.

Check your answer

Guided solution: The intended variable is explanation length, and the outcome is performance on the particular understanding task, not all human understanding. Previous experience is a confound because it differs with explanation choice and could explain performance. The available conclusion is that the group choosing the brief explanation performed better in this case; the effect of length alone is unknown. A better comparison keeps content and assessment consistent and randomly assigns participants to lengths, taking experience into account in design and checking implementation. This guarantees neither exact equality of experience nor generalization beyond the club. Describe the sample and investigate relevance to other settings instead of strengthening the wording.

Reference guide: “Analyzing Findings” in OpenStax’s Psychology 2e discusses correlation, experiments, variables, random sampling and random assignment; “Approaches to Research” describes study methods. The calculations and cases in this lesson are original practice materials, and their conclusions are limited by the information supplied.

Lesson summary

Study design shapes the conclusions available. Description shows a pattern, association shows a relationship without establishing its cause, and controlled experiments strengthen inference about an effect while retaining limitations. Sampling concerns who enters a study; random assignment concerns what participants receive within it. Calculate means and medians with units, then return to the data and conditions rather than turning one number into a broad judgment.