3/2/2014
Chi Square Test -- use to compare
actual outcome to expected outcome
Prediction: The placement of stomata
does not depend on the leaf surface.
If this is the case, then the upper
epidermis and the lower epidermis of
a leaf should have the same stomatal
density.
This spreadsheet shows the stomatal
densities (# of stomata per mm2) of
the upper epidermis and lower
epidermis of a Zea mays (corn) leaf.
First, we need to get the averages for
the two sets of stomatal counts.
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To calculate the average #
of stomata per mm2 for
the upper epidermis, click
on an empty cell. In the
example, the cell is A14.
From the menu bar,
select:
Formulas
More Functions
Statistical
AVERAGE
Enter the range of cells whose values are to be averaged in the Number 1 box of the
dialog box. If applicable, enter additional blocks of cells in the Number 2 box.
Click OK.
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Repeat for the cells with the stomatal density counts for the lower epidermis.
The data were reported as whole
numbers of stomata per mm2, no
decimals. Round the average counts to
the nearest whole number. These
rounded averages are the actual
number of stomata per mm2.
Our assumption is that the leaf
surface does not matter. We expect
the densities to be the same on both
the upper and lower epidermis: half
of the total stomata on the upper and
half on the lower, or a 0.5:0.5 ratio.
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To get the p-value for the
Chi square test
Click on an empty cell, in
this case B17.
From the menu bar, select:
Formulas
More Functions
Statistical
CHISQ.TEST
The Chi square dialog box
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Enter the cells with the actual stomatal counts in the <Actual_range> box.
Enter the cells with the expected stomatal counts in the <Expected_range> box.
Then click OK.
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The p-value now appears in cell B17.
To determine if there is a significant
difference between the actual stomatal
counts and the predicted stomatal
counts:
If p≥ 0.05, there is not a significant
difference between actual and
expected.
If p< 0.05, there is a significant
difference between actual and
expected.
The p here is 0.17, which is greater than
or equal to 0.05. Therefore, the actual
counts do not differ significantly from an
expected distribution of equal stomatal
densities on the two epidermides.
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