Research methods: variables, hypotheses, choosing a statistical test and the sign test
Before running a study, researchers must clearly define their variables and hypotheses; afterwards they must choose the correct statistical test to analyse their results. This topic covers identifying independent and dependent variables, writing directional, non-directional and null hypotheses, controlling extraneous variables, and using experimental design and level of measurement to select an appropriate inferential test, including how to carry out and interpret a sign test.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Learn to identify the independent variable (IV) and dependent variable (DV) in a described study, and name the experimental design used (independent groups, repeated measures, or matched pairs).
- Learn to write a fully operationalised hypothesis, in both directional and non-directional form.
- Learn to write the corresponding null hypothesis for a study.
- Learn to identify a plausible extraneous variable in a study and describe a control for it.
- Learn to read a test-choice table by design (independent groups, repeated measures, or correlation) and by level of measurement (nominal, ordinal, or interval/ratio, and whether data is normally distributed) to select the correct inferential test.
- Learn to carry out a sign test: assign a sign to each participant's change, exclude any tied (zero-change) scores, calculate S, and compare it with a critical value.
- Learn to interpret a significant or non-significant result correctly, including the difference between statistical significance and how large or consistent an effect looks in the raw data.
Worked example
A teacher tests whether a short breathing exercise reduces exam stress, using a repeated measures design with six students. Each student rates their stress from 0 (no stress) to 10 (extreme stress) before and after a 10-minute breathing exercise: Student 1: before 8, after 5. Student 2: before 6, after 7. Student 3: before 9, after 4. Student 4: before 7, after 7. Student 5: before 8, after 3. Student 6: before 5, after 2. Using a sign test, decide whether the breathing exercise produced a significant reduction in stress (the critical value of S for n = 5, p < 0.05, one-tailed, is 0).
- Work out the direction of change for each student: Student 1 decrease (-), Student 2 increase (+), Student 3 decrease (-), Student 4 no change (0), Student 5 decrease (-), Student 6 decrease (-).
- Exclude any student showing no change: Student 4 is excluded because their score did not change, leaving n = 5.
- Count how many of the remaining signs are the less frequent sign: there are 4 decreases (-) and 1 increase (+), so the less frequent sign is the +, occurring once.
- State the calculated value of S: S = 1.
- Compare S with the given critical value for n = 5 (which is 0), remembering the result is only significant if the calculated value is less than or equal to the critical value.
- Since S (1) is greater than the critical value (0), state the final decision: the result is not significant, so the null hypothesis is retained: the breathing exercise did not produce a significant reduction in stress in this sample.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a A Level Psychology exam paper, with a full mark scheme.
A researcher tests whether owning a pet (yes or no) is associated with a person's self-reported stress category (low or high), using one sample of adults rather than two separate groups. The calculated chi-squared value is 3.1. The critical value at p < 0.05, for the appropriate degrees of freedom, is 3.84. State whether the result is significant and explain what this means.
A student carries out a repeated measures study comparing 8 participants' reaction times before and after drinking caffeine. The reaction-time data is interval level, but a normality check shows the data is not normally distributed. The student decides to use a related (paired) t-test to analyse the results. Explain why the student's choice of test is incorrect, and identify the test they should have used instead.
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