When do we use it? When there are:
a) Differences between conditions
b) One variable
c) Three conditions (or more)
d) Relateddesign
We will code it like this: KWD13Uor. The “or” comes from ordinal data and means that the KruskalWallis test is nonparametric (i.e. uses ordinal data). Since we are using ordinal data, we would ideally rank the scores like we did in the Friedman test. However, since the Friedman test is unrelated, we cannot do horizontal ranking, instead, we will rank the scores like in the same way we did in the MannWhitney test.
Condition 1  Condition 2  Condition 3  
2  3  11  
3  5  7  
1  6  4  
0  6  8 
And see the computed data below:
Condition 1  Condition 1 Ranks  Condition 2  Condition 2 Ranks  Condition 3  Condition 3 Ranks  
2  3  3  4.5  11  12  
3  4.5  5  7  7  10  
1  2  6  8.5  4  6  
0  1  6  8.5  8  11 
————————————————————————
See the practice data below:
Hypothesis: the number of illustrations in a sheet will affect participants’ recall of words from the text in the sheet.
Since we are not stating the direction of the differences, our hypothesis is twotailed.
Condition 1 (high number of illustrations) 
Condition 1 Ranks  Condition 2 (moderate number of illustrations) 
Condition 2 Ranks  Condition 3 (no illustrations) 
Condition 3 Ranks 

19  14  12  
21  15  12  
17  9  13  
16  10 
From the above table, we calculate:
 Ranks columns
 Means for every condition
 Ranks total for every condition
Condition 1 (high number of illustrations)  Condition 1 Ranks  Condition 2 (moderate number of illustrations) 
Condition 2 Ranks  Condition 3 (no illustrations) 
Condition 3 Ranks  
19  10  14  14  12  3.5  
21  11  15  15  12  3.5  
17  9  9  9  13  5  
16  8  10  2  
Ranks Totals  38  14  14  
Means  18.25  12.67  11.75 
We see that on average, the number of illustrations did affect participants’ recall of words from the text as we can see differences in word recall among conditions. But we need to check whether or not these differences are statistically significant. So we will use the KruskalWallis test.
Rationale of the KruskalWallis test (related)
The KruskalWallis test aims to find out whether the rank totals are different for the three conditions. If the differences between the rank totals are due to random factors (as stated by the null hypothesis), the differences across the conditions would be relatively small. In that case, the null hypothesis could be rejected.
N = Number of participants
n = number of participants in each condition
∑T² = Sum of Squared Rank Totals (for all conditions)
The KruskalWallis Test Table
The KruskalWallis Critical Values Table (I have not found any straightforward table so I will upload one myself soon) enables you to check whether given your one/two tailed hypothesis, your value and your sample size, the probability that the differences found between conditions were likely to occur by chance.
We open up the table and we check against our df (number of conditions – 1) and our H value (7.2). Our value has to be equal or larger than the values in the table. The critical value with our sample size is 5.99. Our value is larger than 5.99 so the probability that the differences found between conditions can occur due to chance is less than 5%, this enables us to claim that the differences are statistically significant and thus we can reject the null hypothesis.
In our case, taking a look at the means, the data shows that more words were recalled from the highly illustrated sheet than from the other two sheets, and we know that the differences are statistically significant (p < 0.05).
Note: The KruskalWallis test can only test twotailed hypothesis.