Name: ______Date: ______Block: ______

Critical values
p value
df / 0.25 / 0.2 / 0.15 / 0.1 / 0.05 / 0.025 / 0.02 / 0.01 / 0.005 / 0.0025 / 0.001 / 0.0005
1 / 1.32 / 1.64 / 2.07 / 2.71 / 3.84 / 5.02 / 5.41 / 6.63 / 7.88 / 9.14 / 10.83 / 12.12
2 / 2.77 / 3.22 / 3.79 / 4.61 / 5.99 / 7.38 / 7.82 / 9.21 / 10.6 / 11.98 / 13.82 / 15.2
3 / 4.11 / 4.64 / 5.32 / 6.25 / 7.81 / 9.35 / 9.84 / 11.34 / 12.84 / 14.32 / 16.27 / 17.73
4 / 5.39 / 5.59 / 6.74 / 7.78 / 9.49 / 11.14 / 11.67 / 13.23 / 14.86 / 16.42 / 18.47 / 20
5 / 6.63 / 7.29 / 8.12 / 9.24 / 11.07 / 12.83 / 13.33 / 15.09 / 16.75 / 18.39 / 20.51 / 22.11

How to Use the Chi-Squared Distribution

Down and Dirty: Using the probability of 0.05, simply compare your calculated X2 to the critical value in the table. If your calculated X2 critical value, then reject the null hypothesis. If your calculated X2 is < critical value, accept the null hypothesis.

Form a more mathematical explanation and math geeks: The relative standard commonly used in biological research isp >0.05. The p value is theprobabilitythat the deviation of the observed from that expected is due to chance alone (no other forces acting). In this case, usingp0.05, you would expect any deviation to be due to chance alone 5% of the time or less. When p > 0.05 the null hypothesis is accepted and there is no significant difference between expected and observed. Any differences are just due to chance. Of course when p < 0.05, the null hypothesis would be rejected and there is a significant difference between the observed and expected.

Examples:

·  Imagine you calculate a X2 of 2.668 for a set of data with two categories. Refer to a chi-square distribution table. Using the appropriate degrees of freedom, locate the value closest to your calculated chi-square in the table. Determine the closest p(probability) value associated with your chi-square and degrees of freedom. In this case (X2=2.668), the p value is about 0.10, which means that there is a 10% probability that any deviation from expected results is due to chance only. Based on our standard p0.05, this is within the range of acceptable deviation. In terms of the null hypothesis, you would accept the null hypothesis.

·  If your degree of freedom is 2 and your calculated X2 is 9.10, then your probability (p) would be between 0.02 and 0.01. This would besignificant because p < 0.05. Therefore the null hypothesis would be rejected.