# TWIN STUDIES.STATISTICS

```CONCORDANCE
DISCORDANCE
TWIN STUDIES:
AND
CONCORDANCE
◦ The presence of the same trait in both members of a
pair twins
Ex.
◦ Identical twins
DISCORDANCE
◦ Twin pairs do not have the same trait
Ex.
◦ Fraternal twins
PROBABILITY STATISTICAL TESTING
AND
Level of Significance
◦ Say
that
you
are
performing
a genetic cross in which you know
the genotypes of the parents. In this
situation, you might hypothesize that
the cross will result in a certain ratio
of phenotypes in the offspring. But
what if your observed results do not
How
can
you
tell
whether
deviation was due to chance?
this
◦Once you have performed an experiment, how
can you tell if your results are significant?
Chi-square Test
◦ Used to see if observed values for a set of data are
similar or significantly different from expected values
The chi-square value is calculated using the following formula:
Using this formula, the difference between the observed and expected frequencies is
calculated for each experimental outcome category. The difference is then squared and
divided by the expected frequency. Finally, the chi-square values for each outcome are
summed together, as represented by the summation sign (Σ).
Chi-square test can only be applied to numbers of progeny, not to proportions or
percentages.
◦ Recall that when Mendel crossed his pea plants, he learned that tall (T)
was dominant to short (t). You want to confirm that this is correct, so
you start by formulating the following null hypothesis: In a cross
between two heterozygote (Tt) plants, the offspring should occur in a
3:1 ratio of tall plants to short plants. Next, you cross the plants, and
after the cross, you measure the characteristics of 400 offspring. You
note that there are 305 tall pea plants and 95 short pea plants; these
are your observed values. Meanwhile, you expect that there will be 300
tall plants and 100 short plants from the Mendelian ratio.
◦ you have to choose a critical value at which to reject your
null hypothesis. You opt for a critical value probability of 0.01
(1%) that the deviation between the observed and expected
values is due to chance. This means that if the probability is
less than 0.01, then the deviation is significant and not due to
chance, and you will reject your null hypothesis. However, if
the deviation is greater than 0.01, then the deviation is not
significant, and you will not reject the null hypothesis.
So, should you reject your null hypothesis or not? Here's a summary of your observed
and expected data:
Tall
Short
Expected
300
100
Observed
305
95
Now, let's calculate Pearson's chi-square:
•For tall plants: Χ2 = (305 - 300)2 / 300 = 0.08
•For short plants: Χ2 = (95 - 100)2 / 100 = 0.25
•The sum of the two categories is 0.08 + 0.25 = 0.33
•Therefore, the overall Pearson's chi-square for the experiment is Χ2 = 0.33
Table 1: Chi-Square Table
DegreesProbability (P)
0.99
of0.995
Freedom
(df)
1
----2
0.010
0.020
3
0.072
0.115
4
0.207
0.297
5
0.412
0.554
6
0.676
0.872
7
0.989
1.239
8
1.344
1.646
9
1.735
2.088
10
2.156
2.558
11
2.603
3.053
12
3.074
3.571
13
3.565
4.107
14
4.075
4.660
15
4.601
5.229
16
5.142
5.812
17
5.697
6.408
18
6.265
7.015
19
6.844
7.633
0.975
0.95
0.90
0.10
0.05
0.025
0.01
0.005
0.001
0.051
0.216
0.484
0.831
1.237
1.690
2.180
2.700
3.247
3.816
4.404
5.009
5.629
6.262
6.908
7.564
8.231
8.907
0.004
0.103
0.352
0.711
1.145
1.635
2.167
2.733
3.325
3.940
4.575
5.226
5.892
6.571
7.261
7.962
8.672
9.390
10.117
0.016
0.211
0.584
1.064
1.610
2.204
2.833
3.490
4.168
4.865
5.578
6.304
7.042
7.790
8.547
9.312
10.085
10.865
11.651
2.706
4.605
6.251
7.779
9.236
10.645
12.017
13.362
14.684
15.987
17.275
18.549
19.812
21.064
22.307
23.542
24.769
25.989
27.204
3.841
5.991
7.815
9.488
11.070
12.592
14.067
15.507
16.919
18.307
19.675
21.026
22.362
23.685
24.996
26.296
27.587
28.869
30.144
5.024
7.378
9.348
11.143
12.833
14.449
16.013
17.535
19.023
20.483
21.920
23.337
24.736
26.119
27.488
28.845
30.191
31.526
32.852
6.635
9.210
11.345
13.277
15.086
16.812
18.475
20.090
21.666
23.209
24.725
26.217
27.688
29.141
30.578
32.000
33.409
34.805
36.191
7.879
10.597
12.838
14.860
16.750
18.548
20.278
21.955
23.589
25.188
26.757
28.300
29.819
31.319
32.801
34.267
35.718
37.156
38.582
◦ At the beginning of your experiment, you decided that if the probability was
less than 0.01, you would reject your null hypothesis because the deviation
would be significant and not due to chance. Now, looking at the row that
corresponds to 1 degree of freedom, you see that your calculated chi-square
value of 0.33 falls between 0.016, which is associated with a probability of 0.9,
and 2.706, which is associated with a probability of 0.10. Therefore, there is
between a 10% and 90% probability that the deviation you observed between
your expected and the observed numbers of tall and short plants is due to
chance. In other words, the probability associated with your chi-square value
is much greater than the critical value of 0.01. This means that we will not
reject our null hypothesis, and the deviation between the observed and
expected results is not significant.
Sources
◦ https://www.nature.com/scitable/topicpage/genetics-and-statistical-analysis-34592
◦ https://www.healthychildren.org/English/family-life/family-dynamics/Pages/TheDifference-Between-Identical-and-Fraternal-Twins.aspx
◦ https://www.britannica.com/science/dizygotic-twin
```
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