The Friedman test is a nonparametric analysis of a randomised block experiment. Its parametric counterpart is the Two-Way Analysis of Variance. It requires the data to be balanced (all factor combinations must have the same number of observations).
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Null Hypothesis, H0 |
Alternate Hypothesis, H1 |
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All treatment effects = 0 |
All treatment effects ¹ 0 |
1. Choose ProcessMA > Statistics > Nonparametric > Friedman.
2. In Response, select the column containing the response.
3. In Treatment, select the column containing the treatment levels.
4. In Blocks, select the column containing the block levels.
5. Click OK.
Note To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.
Response: Numeric.
Treatment: Text or Numeric; Must have the same number of data points as the variable; Must contain at least 2 distinct categories.
Blocks: Text or Numeric; Must have the same number of data points as the variable; Must contain at least 2 distinct categories.
You want to conduct an experiment to assess the strength of concrete with different types of hardener. You prepared 15 blocks of concrete using three types of hardener on five different batches of cement, and tested their strengths.
1. Open worksheet ProcessMA > Tools > Data Files > Stat.xls.
2. Choose ProcessMA > Statistics > Nonparametric > Friedman.
3. In Response, select AA – Strength.
4. In Treatment, select AB – Hardener.
5. In Blocks, select AC – Batch.
6. Click OK.
Interpretation
For a desired a = 0.05, since p = 0. 4493 > a, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the treatment effects are not zero.