80 lines
2.5 KiB
Markdown
80 lines
2.5 KiB
Markdown
[[G11 Pre-AP Biology]]
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Punnet squares determines if there is a significant relationship between observed data and expected data.
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Example begin:
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let yellow be rep recessive allel y
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let green rep allele for Y
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p1: Yy x Yy
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gametes: Y, y x Y, y
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Example end.
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Chi square tutorial.
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Start off with two hypothesis.
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Null hypothesis ($H_0$):
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"There is not significant difference between observed and expected values of 75 yellow, 25 green peas. The differences are due to random chance alone."
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Alternative hypothesis ($H_A$):
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"There is a significant difference between the observed and expected values of 85, 25 green peas"
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Find the degrees of freedom and critical value.
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Degree of freedom: Number of categories/classes subtract 1.
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In the example, the 2 categories would have a degree of freedom of 1.
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Find the critical value. Find p=0.05 and degree of freedom.
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If the Chi Square is less than the critical value, accept the null hypothesis.
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Else accept alternative hypothesis.
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Chi square formula:$$\Sigma\frac{(o-e)^2}{e}$$
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![[Pasted image 20261026103929.png]]For the example, the formula results in 1.92, which is less than 3.84, thus it's failed to reject null hypothesis.
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An example conclusion for the example is "Fail to reject null hypothesis. The $x^2$ is smaller than the critical value of 3.841. There is not significant difference between the observed and expected values of yellow to green peas."
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Example begin:
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Let C represent purple.
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Let c represent corn.
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Let W represent wrinkled.
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Let w represent smooth.
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P1: CcWw x ccww
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Gametes:
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C, c, W, w x c,c,w,w
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| | CW | Cw | cW | cw |
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| --- | ---- | ---- | ---- | ---- |
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| cw | CcWw | Ccww | ccWw | ccww |
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Genotypes:
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25% Ccww
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25% ccWw
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25% ccww
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25% CcWw
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Phenotypes:
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25% purple smooth corn.
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25% yellow wrinkled corn.
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25% yellow smooth corn.
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25% purple wrinkled corn.
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Hypothesis:
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null
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not null
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Degree of freedom is 3.
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Critical value is 7.82.
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Expected 200 purple smooth, 200 yellow wrinkled, 200 yellow smooth 200 purple wrinkled.
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Results are 200 purple wrinkled 200 purple smooth 190 yellow wrinkled 189 yellow smooth.
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| Phenotype | Observed | Expected | $\frac{(o-e)^2}{e}$ |
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| --------------- | -------- | -------- | ------------------- |
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| purple wrinkled | 200 | 195 | 0.1282 |
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| purple smooth | 200 | 195 | 0.1282 |
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| yellow wrinkled | 190 | 195 | 0.1282 |
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| yellow smooth | 189 | 195 | 0.1846 |
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| | 779 | | 0.5692 |
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0.5692 is less than the critical value of 7.82, thus null hypothesis.12
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