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Line 274: − − ==Comparison of p-Values== − − The following table compares the p-values reported in Table 2 of Blount et al. to the chi-square p-values for the same experiments. For experiments one and three, the chi-square p-values are much larger than the "mean generation" test p-values from the paper. − − {|class="wikitable" style="text-align:center" − |- − | − !Experiment 1 − !Experiment 2 − !Experiment 3 − |- − !p-Value from Paper − |0.0085 − |0.0007 − |0.082 − |- − !Chi-square p-value − |0.19 − |0.0004 − |0.22 − |} − − The chi-square test p-values are computed by comparing the test statistic to the chi-square distribution. It is generally assumed that the cell frequencies should be greater than five so that the statistic's distribution follows chi-square distribution. However, there is no consensus about what minimum cell frequency is necessary or how many expected values need to cross that threshold.
Significance of E. Coli Evolution Experiments (view source)
Revision as of 13:34, July 2, 2009
, 13:34, July 2, 2009Put p-value comparison table closer to beginning
\left(p_i-\bar{p}\right)^2>0</math> where <math>\bar{p}</math> is the mean of the success probabilities). Thus the chi-square test is an effective hypothesis test for the data and hypotheses from Blount et al.
\left(p_i-\bar{p}\right)^2>0</math> where <math>\bar{p}</math> is the mean of the success probabilities). Thus the chi-square test is an effective hypothesis test for the data and hypotheses from Blount et al.
==Experiment One Data==
==Comparison of p-Values==
The following table compares the p-values reported in Table 2 of Blount et al. to the chi-square p-values for the same experiments. For experiments one and three, the chi-square p-values are much larger than the "mean generation" test p-values from the paper.
{|class="wikitable" style="text-align:center"
|-
|
!Experiment 1
!Experiment 2
!Experiment 3
|-
!p-Value from Paper
|0.0085
|0.0007
|0.082
|-
!Chi-square p-value
|0.19
|0.0004
|0.22
|}
The chi-square test p-values are computed by comparing the test statistic to the chi-square distribution. It is generally assumed that the cell frequencies should be greater than five so that the statistic's distribution follows chi-square distribution. However, there is no consensus about what minimum cell frequency is necessary or how many expected values need to cross that threshold.
===Experiment One Data===
The data from experiment one of the paper is shown below (see Table 1 of the paper). The expected outcomes under the null hypothesis (no evolutionary innovation occurs) are also shown.
The data from experiment one of the paper is shown below (see Table 1 of the paper). The expected outcomes under the null hypothesis (no evolutionary innovation occurs) are also shown.
The chi-square test is a common statistical method.<ref>''Mathematical Statistics with Applications'' by Wackerly, Mendenhall, and Scheaffer, Section 14.4.</ref> It can be implemented in Microsoft Excel. If the numbers from the last four columns of the experiment one data table (excluding the “totals” row) are entered into Excel in rows 1-12 and columns A-D, then the p-value can be computed by entering “=CHITEST(A1:B12,C1:D12)” into any empty cell of the spreadsheet.
The chi-square test is a common statistical method.<ref>''Mathematical Statistics with Applications'' by Wackerly, Mendenhall, and Scheaffer, Section 14.4.</ref> It can be implemented in Microsoft Excel. If the numbers from the last four columns of the experiment one data table (excluding the “totals” row) are entered into Excel in rows 1-12 and columns A-D, then the p-value can be computed by entering “=CHITEST(A1:B12,C1:D12)” into any empty cell of the spreadsheet.
==Experiment Three Data==
===Experiment Three Data===
The experiment three data from Blount et al. is shown in the table below. The expected numbers of mutants under the null hypothesis (constant mutation rate) is also shown.
The experiment three data from Blount et al. is shown in the table below. The expected numbers of mutants under the null hypothesis (constant mutation rate) is also shown.
!2792
!2792
|}
|}
==References==
==References==