Introduction to Non-parametric Tests

In general, non-parametric tests:

  • make few or no assumptions about the distribution of the data
  • reduce the effect of outliers and heterogeneity of variance
  • can often be used even for ordinal, and sometimes even nominal, data

Since non-parametric tests do not estimate population parameters, in general there are

  • no estimates of variance/variability
  • no confidence intervals
  • fewer measures of effect size

Also non-parametric tests are generally not as powerful as parametric alternatives when the assumptions of the parametric tests are met.

In this part of the website we study the following non-parametric tests:

Elsewhere in the website we look at the following additional non-parametric tests:

As we will see, many of the non-parametric tests are based on analysis of the ranks of the data elements, often comparing the median instead of the mean.

8 Responses to Introduction to Non-parametric Tests

  1. Nasam Atukun says:

    Dear Charles,

    Need some advice for my study.
    I have data of exercise study after chest operation, where I took physical data for several days towards their full recovery. In this study, I would like to know whether or not certain exercise, let say breathing in regards with lung volume, will lead to full recovery after 6-days post-operative.
    So, I have data of the lung volume of several patients from day-1 to day-5 post-operation, and within those data, I have those patients who successfully recovered after day-5 and those who failed. The distribution of daily data among patients are very wide, the standard deviation are big.
    My question is, what statistical analysis is needed to be done in order to see the correlation of daily data (i.e. lung volume) with the successful recovery?

    Thank in advance for your advice,

  2. Dr buenos días, por favor me aclara, si para una investigación donde se debe comparar un grupo de individuos en tres ocasiones diferentes, que responden a una encuesta de mejoramiento en salud, es apropiado aplicar una prueba de Mc Nemar dos veces, para comparar en tres ocasiones los mismos individuos.
    Que pena otra pregunta, en el Análisis de Componentes principales, como podría hacer la gráfica de vectores?
    Muchas gracias

    Dr Good morning, please clarify, if for an investigation where a group of individuals must be compared on three different occasions, which respond to a health improvement survey, it is appropriate to apply a Mc Nemar test twice, in order to compare in Three occasions the same individuals.
    Excuse me another question, in the main Component Analysis, how could the vector graphics do?
    Thank you very much

    • Charles says:

      Sorry, but I don’t understand the situations well enough to provide an answer.

      • Dr gracias, solo es comparar tres veces el mismo conjunto de individuos con respuestas binarias (Lo ideal sería la prueba de Cocharn, creo)

        Pero, una pregunta que me surge en ACP es podría hacer el gráfico de ACP con vectores?

        Dr thanks, it’s just compare three times the same set of individuals with binary answers (The ideal would be Cocharn’s test, I think)

        But, one question that arises in ACP is, could I make the ACP chart with vectors?

  3. Mitra Jazayeri says:

    Hi Charls,
    If i have unequal variances and non-normal distributions and unequal sample sizes, what analysis should i do instead of two way anova? Or will that still be valid with an stringent significance level?

    • Charles says:

      I don’t know of a non-parametric test for this. One approach that might work for you is to use Two Factor ANOVA with the Regression option (since the sample sizes are unequal) and then ignore the omnibus test results and instead focus on the follow-up tests. Games-Howell might be the best test in this case.

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