Statistical Analysis

Mohd Aminudin Bin Mustapha

Centre for Pre-University Studies

Universiti Malaysia Sarawak

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Learning Objectives

• Describe relationship of genetic and

statistic

• Apply chi-square test in genetic problem.

Genetics and Statistical Analysis

Once you have performed an experiment, how can you

tell if your results are significant?

For example, say that you are performing a genetic

cross in which you know the genotypes of the parents

You might hypothesize that the cross will result in a

certain ratio of phenotypes in the offspring.

Genetics and Statistical Analysis

If your observed results do not exactly match your

expectations?

How can you tell whether this deviation was due to

chance?

The key to answering these questions is the use

of statistics, which allows you to determine whether your

data are consistent with your hypothesis.

Forming and Testing a

Hypothesis • The first thing any scientist does before performing an

experiment is to form a hypothesis about the experiment's outcome.

• Form of a null hypothesis, which is a statistical hypothesis that provides the expected values for an experiment.

• Null hypothesis is proposed by a scientist before completing an experiment, and it can be supported by data or disproved in favor of an alternate hypothesis.

• Then an experiment can be designed to determine whether the data confirm or reject the hypothesis.

Chi-Square

Pearson's chi-square test is used to examine the role of

chance in producing deviations between observed and

expected values.

The test indicates the probability that chance alone

produced the deviation between the expected and

the observed values

When the probability calculated from Pearson's chi-

square test is high, it is assumed that chance alone

produced the difference.

Conversely, when the probability is low, it is assumed

that a significant factor other than chance produced the

deviation.

Degrees of Freedom

A critical factor in using the chi-square test is the “degrees of freedom”, which is essentially the number of independent random variables involved.

Degrees of freedom is simply the number of classes of offspring minus 1.

For our example, there are 2 classes of offspring: purple and white. Thus, degrees of freedom (d.f.) = 2 -1 = 1.

Critical Chi-Square

Critical values for chi-square are found on tables, sorted by degrees of freedom and probability levels. Be sure to use p = 0.05. (to success, error occur not more than 5%/0.05)

If your calculated chi-square value is greater than the critical value from the table, you “reject the null hypothesis”.

If your chi-square value is less than the critical value, you “fail to reject” the null hypothesis (that is, you accept that your genetic theory about the expected ratio is correct).

Pearson's Chi-Square Test for

Goodness-of-Fit Pearson's chi-square test works well with genetic data

as long as there are enough expected values in each

group.

In the case of small samples (less than 10 in

any category) that have less than 1 degree of freedom,

the test is not reliable.

Chi-square test can only be applied to numbers

of progeny, not to proportions or percentages.

Question

• Consider these results among the F2

4,400 yellow seeds

1,624 green seeds

What is the calculated chi-square value?

Answer

Phenotypes O E O-E (O-E)2 (O-E)2 E

Yellow 4400 6024 X 3/4 4518

4400 - 4518 -118

-1182 13,924

13924 / 4518 3.08

Green 1624 6024 X 1/4 1506

1624 -1506 -118

-1182 13,924

13924 /1506 9.24

Total 6024 6024 12.32

Question

• Consider these results from a dihybrid cross

30 red tall

65 white tall

83 red short

206 white short

What is calculated chi-square value?

Answer

Phenotypes O E O-E (O-E)2 (O-E)2 E

White and short (W-S-)

206 24 X 9 216

206 - 216 10

102 100

100 / 216 0.463

Red and short (wwS-)

83 24 X 3 72

83 - 72 11

112 121

121 / 72 1.681

White and tall (W-ss)

65 24 X 3 72

65 - 72 -7

-72 49

49 / 72 0.681

Red and tall (wwss)

30 24 X 1 24

30 - 24 6

62 36

36 / 24 1.500

Total 384 384 4.325