This is the sixth and penultimate step in constructing the oneway advisor. The advisor automates four tests associated with the assumptions of a oneway analysis of variance. In this step a test will be performed to assess whether the data within each level of the grouping variable have equal variance.

## Testing For Equal Variance

This test is performed in JMP by selecting the *Unequal Variance* option from the red triangle option within the Oneway platform. Here is some sample output:

It seems that our professors of statistics can’t quite agree on how to perform this test! I can think of three ways of dealing with this table of information:

- Decide on a standard test .e.g Levene and only look at the p-value associated with this test
- Apply contextual knowledge – e.g. use the Bartlett test if the data have been demonstrated to be normally distributed, otherwise use the Levene test
- Take the worse-case outcome i.e. look at all the tests and select the lowest p-value

I’m going to choose to implement the third option.

A couple of points that will become relevant to the code implementation:

- The above table is contained within an outline box called “Tests that the Variances are Equal”
- If the grouping variable has more than two levels then the p-Value column takes the label “Prob > F” as illustrated below:

## Checking the Number of Levels

Given that the output differs based on the number of levels within the grouping variable we’ll need some code to find the number of levels . There are a lot of interesting ways to implement this in code and we could go on quite a tangent exploring all the methods – but to keep the discussion focussed I’m just going to state the following code without too much justification, other than it works:

1 2 |
Summarize(levels = By( Column(dt,xCol)) ); numLevels = NITems(levels); |

Where **dt** is a reference to a data table and **xCol** is the string name of a column. You can verify the code by opening the “Big Class” data table and running this code:

1 2 3 4 5 |
dt = current data table(); xCol = "sex"; Summarize(levels = By( Column(dt,xCol)) ); nLevels = NITems(levels); show(levels,nLevels); |

Here is the JMP log window output:

## Test Equal Variances

Here is the code for the implementation of the user-defined function **Test Equal Variances**. The code needs to be added to the file *Analysis Components.jsl*.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 |
Test Equal Variances = Function({dt,yCol,xCol},{Default Local}, Summarize(levels = By( Column(dt,xCol)) ); nLevels = NITems(levels); ow = dt << Oneway( Invisible, Y( Eval(yCol) ), X( Eval(xCol) ), Unequal Variances( 1 ), ); rep = ow << Report; ob = rep["Tests that the Variances are Equal"]; tb = ob[TableBox(2)]; If (nLevels==2, cbPValue = tb[NumberColBox("p-Value")]; , cbPValue = tb[NumberColBox("Prob > F")]; ); lstPValues = cbPValue << Get; pValue = Min(lstPValues); rep << Close Window; Return(pValue); ); |

- Lines 3 and 4 contain the code illustrated earlier for determining the number of levels in the x-variable
- Lines 5 to 9 create a Oneway object
- Line 8 is the code equivalent of selecting
*Unequal Variance*option found under the red triangle - Line 10 creates the variable rep which is a reference to the window containing the Oneway results
- Line 11 gets a reference to the outline box containing the tabulated results
- Line 12 gets a reference to the table containing the results
- Line 14 creates a variable
that references the p-value column in the results table, if the number of levels is 2**cbPValue** - Line 16 creates a variable
that references the “Prob > F” column if the number of levels is not 2**cbPValue** - Line 18 gets a list of p-values from the column referenced by
**cbPValue** - The variable lstPValues created in line 18 is a list. The Min function identifies the smallest item in this list which is stored in the variable pValue

## Implementing the Function

Now that the test is implemented in code and saved within the *Analysis Components* JSL file, it is available for use within the main code (*step5.jsl*) of the oneway advisor. To use the function the same pattern of code is used as for the tests described in the last two posts. The revisions are highlighted below:

72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 |
// Check assumptions alpha = 0.05; dt = Data Table(dtName); arrPValues = Test Normal Each Level(dt,yColName,xColName); minPValue = Min( arrPValues<<Get Values ); If (minPValue<=alpha, btnNormalLevels << Set Icon(nsICONS:FAIL_ICON) , btnNormalLevels << Set Icon(nsICONS:PASS_ICON) ); strTip = "p-value=" || Char(Round(minPValue,4)) || ".\!N" || "This is the smallest p-value for all the tests \!N" || "(one for each level of the grouping variable). \!N" || "For a test of normality, small p-values imply \!N" || "that the data are not normally distributed."; btnNormalLevels << Set Tip(strTip); pValue = Test Normal Oneway Residuals(dt,yColName,xColName); If (pValue<=alpha, btnNormalResids << Set Icon(nsICONS:FAIL_ICON) , btnNormalResids << Set Icon(nsICONS:PASS_ICON) ); strTip = "p-value=" || Char(Round(pValue,4)) || ".\!N" || "For a normality test, small p-values imply that\!N" || "the data are not normally distributed."; btnNormalResids << Set Tip(strTip); pValue = Test Equal Variances(dt,yColName,xColName); If (pValue<=alpha, btnEqualVariance << Set Icon(nsICONS:FAIL_ICON) , btnEqualVariance << Set Icon(nsICONS:PASS_ICON) ); strTip = "p-value=" || Char(Round(pValue,4)) || ".\!N" || "For a test of variance, small p-values imply that\!N" || "the variances are not equal across the levels."; btnEqualVariance << Set Tip(strTip); |

One the revisions have been made the file should be saved as *step6.jsl*.

## The Output

The oneway advisor is almost complete. Here is what the output should look like:

## One thought on “Testing For Equal Variance”