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Levels of measurement, probability and significance

Edexcel IAL Psychology · WPS01 Social and Cognitive Psychology

Spec 2.2.12 (List B): levels of measurement, probability and significance levels (p ≤ .10, .05, .01), observed and critical values, one- and two-tailed tests, and Type I and Type II errors.

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Levels of measurement

Nominal: data in categories, counted (for example, obeyed or refused). Average: mode.
Ordinal: data that can be put in rank order, but the gaps between points are not equal (Likert ratings, positions in a race). Average: median.
Interval: equal units on a scale, with no true zero (temperature in Celsius). Ratio: equal units with a true zero (time, number of words recalled). Average: mean.

The level of measurement helps choose the test: the Wilcoxon signed ranks test needs at least ordinal data, a test of difference and a repeated measures (or matched pairs) design.

Probability and significance

Inferential tests tell us how likely it is that a difference this large would happen by chance if the null hypothesis were true.

p ≤ .05 (the usual level in psychology): a 5% or less probability the result is due to chance. If met, the result is significant: reject the null hypothesis and accept the experimental (alternative) hypothesis.
p ≤ .01: stricter, 1% or less; used when a mistake would be serious or the research is new or controversial.
p ≤ .10: more lenient, 10%; a greater risk of a chance result being called significant.

The observed (calculated) value from the test is compared with a critical value from a table, using N, the significance level and whether the hypothesis is one- or two-tailed. Sense check: for a one-tailed test, the results must go in the predicted direction.

Type I and Type II errors

Type I error (false positive): rejecting the null hypothesis when it is actually true; claiming an effect that is really chance. More likely with a lenient level such as p ≤ .10.
Type II error (false negative): accepting the null hypothesis when it is actually false; missing a real effect. More likely with a strict level such as p ≤ .01.

p ≤ .05 is a compromise between the two risks.

Worked example

A researcher sets p ≤ .01 and finds her result is not significant, although a real effect exists. What error has she made and why was it more likely?

She accepted the null hypothesis when it was false.
This is a Type II error.
A strict level like p ≤ .01 makes it harder to reach significance, so real effects are more often missed.

Answer: A Type II error, made more likely by the strict significance level.

Key idea: Nominal (categories), ordinal (ranks, unequal gaps), interval/ratio (equal units). p ≤ .05 = 5% chance. Compare observed value with critical value. Type I = false positive (lenient level); Type II = false negative (strict level).

Check yourself

Participants rate their confidence on a scale of 1 to 10. What level of measurement is this?
- Nominal
- Ordinal
- Ratio
- Interval with a true zero
Show answer
Ordinal. Ratings can be ranked, but the gaps are not known to be equal.
Recording whether each participant obeyed or refused gives which level of data?
- Ordinal
- Interval
- Ratio
- Nominal
Show answer
Nominal. Categories that are counted.
What is a Type I error?
- Accepting the null hypothesis when it is false
- Rejecting the null hypothesis when it is true
- Using the wrong sampling method
- Choosing a two-tailed test
Show answer
Rejecting the null hypothesis when it is true. A false positive: claiming an effect that is due to chance.
Which significance level gives the greatest risk of a Type I error?
- p ≤ .05
- p ≤ .01
- p ≤ .10
- p ≤ .001
Show answer
p ≤ .10. The more lenient the level, the easier it is to call a chance result significant.
Express the significance level p ≤ .05 as a percentage probability that the result is due to chance.
Show answer
5 %. 0.05 x 100 = 5%.
p ≤ .01 means a 1 in how many chance (or less) that the result occurred by chance?
Show answer
100. 0.01 = 1/100, so 1 in 100.
Explain what a Type II error is.
Show answer
A Type II error is accepting the null hypothesis when it is actually false, so a real effect or difference is missed (a false negative).. Type II: accepting a false null hypothesis.

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Last updated 8 November 2026. Spotted a mistake? Tell us.