Non-Parametric Tests

Non-Parametric Tests in Psychology

Non-parametric tests are used as an alternative when Parametric Tests cannot be carried out.

Non-parametric tests include the Kruskal-Wallis and the Spearman correlation. These are used when the alternative parametric tests (e.g. one-way ANOVA and Pearson correlation) cannot be carried out because the data doesn’t meet the required assumptions.

Application of Non-Parametric Tests

Non-parametric tests determine the value of data points by assigning + or - signs based on the data ranking. The analysis process involves numerically ordering data and identifying its ranking number.

Data is assigned a ‘+’ if it is greater than the reference value (where the value is expected/hypothesised to fall) and a ‘-’ if it is lower than the reference value. This ranked data becomes the data points for a non-parametric statistical analysis.

Non-Parametric Test: Examples

The example data set illustrates how non-parametric tests are ranked:

Data set: 25, 16, 6, 16, 30. The predicted reference value is 20.

The predicted reference value is 20; therefore, 25 and 30 have positive values, and the rest have negative values.

Non-Parametric: Assumptions

Non-parametric tests are tests with fewer restrictions than parametric tests. It is appropriate to use non-parametric tests in research in different cases. For example:

• When data is nominal, data is nominal when assigned to groups; these groups are distinct and have limited similarities (e.g. responses to ‘What is your ethnicity?’)

• When data is ordinal, that is when data has a set order or scale (e.g. ‘Rate your anger from 1-10’.)

• When there are outliers identified in the data set

• When the data is collected from a small sample

However, it is important to note that non-parametric tests are also used when the following criteria can be assumed:

• At least one violation of parametric tests assumptions. E.g., data should have similar homoscedasticity of variance: the amount of ‘noise’ (potential experimental errors) should be similar in each variable and between groups.

• Non-normal distribution of data. In other words, data is likely skewed.

• Randomness: data should be taken from a random sample from the target population.

• Independence: the data from each participant in each variable should not be correlated; this means that measurements from a participant should not be influenced or associated with other participants.

Difference Between Parametric and Non-Parametric Tests

The table below shows examples of non-parametric tests. It includes their parametric test equivalent, the method of data analysis the test uses, and example research that is appropriate for each statistical test.

Advantages of Non-Parametric Tests

Research using non-parametric tests has many advantages:

• Statistical analysis uses computations based on signs or ranks. Thus, outliers in the data set are unlikely to affect the analysis.

• They are appropriate to use even when the research sample size is small.

• They are less restrictive than parametric tests as they don’t have to meet as many criteria or assumptions. Therefore, they can be applied to data in various situations.

• They have more statistical power than parametric tests when the assumptions of parametric tests have been violated. This is because they use the median to measure the central tendency rather than the mean. Outliers are less likely to affect the median.

• Many non-parametric tests have been a standard in psychology research for many years: the chi-square test, the Fisher exact probability test, and Spearman’s correlation test.

Disadvantages of Non-Parametric Tests

Non-parametric tests also have disadvantages that we should consider:

• The mean is considered the best and a standard measure of central tendency because it uses all the data points within the data set for analysis. If data values change, then the mean calculated will also change. However, this is not always the case when calculating the median.

• As these tests don’t tend to be vastly affected by outliers, there is an increased likelihood of research carrying out a Type 1 error (essentially a ‘false positive’, rejecting the null hypothesis when it should be accepted). This reduces the validity of the findings.

• Non-parametric tests are considered appropriate for hypothesis testing only, as they do not calculate or estimate effect sizes (a quantitative value that tells you how much two variables are related) or confidence intervals. This means that researchers cannot identify how much the independent variable affects the dependent variable and how significant these findings are. Therefore, the utility of the results is limited, and their validity is also challenging to establish.