Non-Parametric Tests

When it comes to statistics, there are many things that we need to consider; this is especially the case when determining whether to use parametric or non-parametric tests. The ultimate goal of researchers is to use parametric tests. However, this is not always possible. And when this is the case, researchers use non-parametric tests.

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Jetzt kostenlos anmeldenWhen it comes to statistics, there are many things that we need to consider; this is especially the case when determining whether to use parametric or non-parametric tests. The ultimate goal of researchers is to use parametric tests. However, this is not always possible. And when this is the case, researchers use non-parametric tests.

- We will start by looking at the use of non-parametric tests in psychology and the application of non-parametric tests. To ensure your understanding, we will then look at non-parametric test examples.
- Then, we will delve into the non-parametric assumptions.
- Moving along, we will explore the difference between parametric and non-parametric tests.
- Finally, we will look at the advantages and disadvantages of non-parametric tests.

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

Non-parametric tests are also known as** distribution-free tests.** These are statistical tests that do not require normally-distributed data.

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

**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.

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

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

X_{1} | X_{2} | X_{3} | X_{4} | X_{5} |

-6 | -16 | -16 | +25 | +30 |

The data is ranked numerically from the lowest (6) to the highest (30). As there are two instances of the value of 16, both are assigned a ranking of 2.5.

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

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

**o****utliers**identified in the data setWhen 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.

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.

Non-parametric test | Equivalent parametric test | Purpose of statistical test | Example |

Wilcoxon rank-sum test | Paired t-test | Compares the mean value of two variables obtained from the same participants | The difference in depression scores before and after treatment |

Mann-Whitney U test | Unpaired t-test | Compares the mean value of a variable measured from two independent groups | The difference between depression symptom severity in a placebo and drug therapy group |

Spearman correlation | Pearson correlation | Measures the relationship (strength/direction) between two variables | The relationship between fitness test scores and the number of hours spent exercising |

Kruskal Wallis test | One-way analysis of variance (ANOVA) | Compares the mean of two or more independent groups (uses a between-subject design, and the independent variable needs to have three or more levels) | The difference in average fitness test scores of individuals who frequently exercise, moderately, or do not exercise |

Friedman’s ANOVA | One-way repeated measures ANOVA | Compares the mean of two or more dependent groups (uses a within-subject design, and the independent variable needs to have three or more levels) | The difference in average fitness test scores during the morning, afternoon, and evening |

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**.

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.

- Non-parametric tests are also known as distribution-free tests. These are statistical tests that do not require normally distributed data.
- 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 their rank number. This ranked data is used as data points for non-parametric statistical analysis.
Examples of non-parametric tests are the Wilcoxon Rank sum test, Mann-Whitney U test, Spearman correlation, Kruskal Wallis test, and Friedman’s ANOVA test. All of these tests have alternative parametric tests.

Non-parametric tests are only used when the assumptions of parametric tests have been violated due to their restrictive nature. Despite this, there are advantages to using non-parametric tests.

Non-parametric tests should be used when data is not normally distributed.

At least one of the assumptions of the parametric test has been violated.

Data is nominal or ordinal.

There are outliers in the data set.

The sample size is small.

When is it appropriate to use non-parametric tests?

- 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

What is the criterion of non-parametric tests?

The following criterion is required for non-parametric tests:

- At least one violation of parametric tests assumptions,
- Non-normally distributed data
- Data is random (taken from random sample)
- Data values are independent from one another (no correlation between data collected from each participant)

Why does data need to be ranked prior to carrying out non-parametric data analysis?

Data needs to be ranked prior to statistical analysis as these ranked values are used as data points for the analysis rather than the raw values obtained from the experiment/observation.

What is the 'reference value'?

The reference value is where the researchers predict/hypothesise where the median value is expected to fall.

Rank the following data values and assign them with the correct sign.

Researchers hypothesised that the reference value would be 13. The dataset is 3, 5, 3, 19, 16, 21, and 14.

-3, -3, -5, +14, +16, +19, +21.

What do '+' and '-' signs mean in terms of ranking data for non-parametric analysis?

Data is assigned as '+' if it is greater than the reference value and ‘-’ if it is lower than the reference value.

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