ANOVA test on dataset

Question

I have a dataset with 3 groups and two variables. I want to do ANOVA test on the three groups for each variable. Does anyone know how to do this?

Needs["ANOVA`"]
ds = Dataset[{
<|"group" -> "1", "var" -> "var1", "value" -> 6.035053959`|>,
<|"group" -> "1", "var" -> "var1", "value" -> 6.193979765`|>,
<|"group" -> "1", "var" -> "var1", "value" -> Missing["UnknownData"]|>,
<|"group" -> "1", "var" -> "var1", "value" -> 3.3745613910000003`|>,
<|"group" -> "2", "var" -> "var1", "value" -> Missing["UnknownData"]|>,
<|"group" -> "2", "var" -> "var1", "value" -> 0.001071983`|>,
<|"group" -> "2", "var" -> "var1", "value" -> 0.00197519`|>,
<|"group" -> "2", "var" -> "var1", "value" -> 0.000850834`|>,
<|"group" -> "3", "var" -> "var1", "value" -> 0.001295309`|>,
<|"group" -> "3", "var" -> "var1", "value" -> 0.000994449`|>,
<|"group" -> "3", "var" -> "var1", "value" -> 0.003818416`|>,
<|"group" -> "3", "var" -> "var1", "value" -> 0.002378116`|>,
<|"group" -> "1", "var" -> "var2", "value" -> Missing["UnknownData"]|>,
<|"group" -> "1", "var" -> "var2", "value" -> 0.00677702`|>,
<|"group" -> "1", "var" -> "var2", "value" -> 0.001844996`|>,
<|"group" -> "1", "var" -> "var2", "value" -> 0.005386635`|>,
<|"group" -> "2", "var" -> "var2", "value" -> 1.320257649`|>,
<|"group" -> "2", "var" -> "var2", "value" -> 1.090243962`|>,
<|"group" -> "2", "var" -> "var2", "value" -> 1.6674887180000002`|>,
<|"group" -> "2", "var" -> "var2", "value" -> 1.88535474`|>,
<|"group" -> "3", "var" -> "var2", "value" -> 0.446011094`|>,
<|"group" -> "3", "var" -> "var2", "value" -> 0.46027675799999995`|>,
<|"group" -> "3", "var" -> "var2", "value" -> Missing["UnknownData"]|>,
<|"group" -> "3", "var" -> "var2", "value" -> 0.344685377`|>}]

I've tried this simple code, but it doesn't work:

ds[GroupBy[#var &], ANOVA["value"]] /@ {"var1", "var2"}

Thanks!

Answer 1

I think there are a few complications to handle. From the code you proposed, it seems to me that you want to run one-way ANOVA on the two subsets obtained by grouping the data according to the value of the "var" key in the full dataset.

However, to carry out one-way analysis, ANOVA accepts input as a list of lists of two elements, not three, as you can see from its documentation. In addition to that, my attempts indicate that ANOVA will also not handle the Missing data points, so they have to be removed.

Here is a sequence of steps I would suggest:

1) Remove missing data that can't be handled by ANOVA:

DeleteMissing[ds, 1, 1]

2) Split the original dataset into two datasets according to the value of the "var" column *)

GroupBy[#"var" &][%]

3) Extract only the first and third columns from each subsets, because the second column containing the "var" value is now the same for all data points in each subset and therefore superfluous:

%[All, #[[All, {1, 3}]] &]

4) Remove the data labels from the associations to prep the data for ANOVA:

%[All, All, Values]

5) Apply one-way ANOVA to each dataset:

Needs["ANOVA`"]
%[All, ANOVA]

The above is shown as a dataset, which truncates some of the results. A more traditional result formatting can be obtained with Normal:

% // Normal