Chi-squared distribution

This test is used when the researcher is testing for a difference, the design is independent measures and the data is nominal. For example, Piaget could have used a chi-squared to test the significance of his data in his three mountains experiment . The design was independent measures because he compared groups of children of different ages and the level of measurement of his data was nominal because the dependent variable was whether the children picked the picture that showed the doll’s view of the model or not. 

<b>Wilcoxon signed ranks test of difference

This test is used when the researcher is testing for a difference, the design is repeated measures and the data is at least ordinal. For example, if the researchers tested children’s social and emotional development using Likert scales from 1-7 before and after a classroom- based mindfulness programme they could test the significance of their data using a Wilcoxon’s signed ranks test of difference.

<b>Spearman’s rank correlation coefficient

This test is used when the researcher is using correlation as the research method and not doing an experiment. Also the data from both variables must be at least ordinal. Correlation is used to test the association or relationship between two measured variables. For example, Ramirez-Esparza and colleagues (2017) tested the correlation between the amount of parentese used when children were 11 months old and their speech production at two years old. Each child therefore had a pair of scores, how much parentese they heard on a daily basis and their level of speech production. These scores could be plotted on scattergrams and then a Spearmans conducted to work out the correlation coefficient, e.g. a number between -1 and +1 which represents the direction (positive or negative) and strength of the correlation (the closer to either -1 or +1 the stronger the relationship).

Observed and critical values

When you conduct an inferential statistical test the final outcome has a different name depending on the test. In Wilcoxon the result is referred to as T, a Spearmans is referred to as r and a chi squared is result is written as Χ². These are all examples of observed values, as they are what we have observed in our data/studies. Once we have an observed value (be it T, r or X²) we can work out our p value. To do this we must compare our observed value with the critical values. To find the correct p value will need to know whether the hypothesis was directional or non-directional and how many participants there were. For Chi-Squared and Spearmans the observed value is significant if it is larger than the critical value and for Wilcoxon the observed value must be less than the critical value to be significant.

Figure 1: Sample critical values table for Spearman’s rank showing the critical values for the 0.05 level of significance with eight participants. In this example, the observed value of r must be greater than 0.643 for a one-tailed test and 0.738 for a two-tailed test. If these values are exceeded then probability can be checked at the 0.025 level, the 0.01 level and so on by comparing with the values in the columns to the right.