AP Biology : Perform chi squared test
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Example Question #1 : Perform Chi Squared Test
In a population of flowers, red is dominant to white. A true-breeding white flower is crossed with a heterozygous flower. Determine the expected ratios of this cross. Given observed values: 63 white flowers, 37 red flowers, determine:
1) The chi squared value
2) The degrees of freedom
3) The p-value
1) 14.44
2) 2
3) p>0.005
1) 6.76
2) 1
3) p>0.025
1) 3.35
2) 4
3) p=0.25
1) 6.76
2) 2
3) p=0.05
1) 6.76
2) 1
3) p>0.025
First, determine the expected ratios using a Punnet Square. Given that red is dominant to white, the genotype of a true-breeding white flower can be denoted rr, and the genotype of a heterozygous flower can be denoted Rr. This cross will produce 50% Rr, 50% rr. Then, converting these percentages to decimals (50%= 0.50), and multiplying by the total population size of the observed population (0.50*100), gives expected values of 50 Rr (red flowers) and 50 rr (white flowers). These expected values and the observed values can then be plugged into the chi square equation 
Example Question #1 : Perform Chi Squared Test
In a chi squared test, the greater the difference between the observed and expected frequencies of a trait, the ___ the p-value.
more positive
more negative
greater
lower
lower
A larger difference between observed and expected values will result in a larger chi square value. Using the critical values table, for a given degrees of freedom, as chi square value increases, p-value decreases.
Example Question #1 : Perform Chi Squared Test
If the p-value determined by a chi-square test is low, which is possible
The null hypothesis is accepted
The alternative hypothesis is rejected
The null hypothesis is rejected
The chi square value is also low
The null hypothesis is rejected
When the p-value is equal to or below the significance level (alpha), the null hypothesis is rejected. For the p-value to be low, the chi square value would need to be large (large difference between observed and expected values). The null hypothesis would not be accepted (under no circumstance is a null hypothesis “accepted”; onlay rejected or failed to reject). The alternative hypothesis would be accepted if the p-value is equal to or below the significance level (alpha).
Example Question #1 : Perform Chi Squared Test
Which of the following chi square values would likely result in rejection of the null hypothesis?
1.97
7.36
13.8
0.35
13.8
A larger difference between observed and expected values will result in a larger chi square value. Using the critical values table, for a given degrees of freedom, as chi square value increases, p-value decreases. A small p-value results in rejection of the null hypothesis.
Example Question #2 : Perform Chi Squared Test
Which is not a possible critical value of a chi square test?
1.8
-1.8
0
180
-1.8
Critical values cannot be negative. The chi squared formula 
Example Question #2 : Perform Chi Squared Test
If the chi square value is larger than the critical value at a given level of significance, what can be stated?
The null hypothesis fails to be rejected
The null hypothesis is accepted
The alternative hypothesis is rejected
The null hypothesis is rejected
The null hypothesis is rejected
If the chi square value is large, this indicates a large difference between the observed and expected values. This will subsequently result in a small p-value when using the critical value table. When the p-value is equal to or smaller than the significance level (alpha), the null hypothesis is rejected.
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