ocw statistical analysis
TRANSCRIPT
Statistical Analysis
Mohd Aminudin Bin Mustapha
Centre for Pre-University Studies
Universiti Malaysia Sarawak
This OpenCourseWare@UNIMAS and its related course materials are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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