Mendelian genetics (Probability value and degree of freedom)

Question

Red Smooth. Red Wrinkled. Yellow smooth yellowwrinkled

#Expected. 25 25 25 25

#observed. 29.6 53.4 7.2. 9.8

X² value. 0.85 32.26 12.67 9.24

The data above is from genetic tracking two traits inherited in Corn.

Based on the data above , you can see that the difference between the expected and predicted outcomes is (a) significant or (b) not significant?

the predicted (a) phenotype or (b) genotype. Suggested that the outcome for each parent is (a) correct or (b) incorrect?

Answer 1

Hi Temitayo!

To find out if your data is significant or not, we need 4 things;

1. The chi square value, denoted as X². Luckily that's already provided in your table! But just a refresher on how this value is obtained, here is the formula
2. X²=(observed-expected)²/(expected)
3. In words, you subtract the expected value from the observed value and square the result of that, then take this value and divide it by the expected
4. for example, lets look at red smooth corn, where expected = 25, and observed = 29.6

X²=(29.6-25)²/25

X²=(4.6)²/25

X²=0.8456

d. To answer if this data set is significant or non-significant, we will add each X² ;

∑X²=0.85+32.26+12.67+9.24

∑X²=55.02

1. We need to know the degrees of freedom (DF), which is found by the following formula
2. DF = (# of expected phenotypes - 1)
3. In words, count the different classes and subtract 1 from that number. To clarify how I mean "expected phenotype", an example would be "red smooth". So we have four total expected phenotypes; red smooth, red wrinkled, yellow smooth, yellow wrinkled.
4. So our DF = (4-1)

DF=3

1. Next we need a chi square table, which can be found online. I am using this one here https://programmathically.com/chi-square-distribution-table/
2. First, find your DF value in the left most column. Remember, our DF is 3.
3. Second, find your chi square (X²) value in the same row as your DF.
4. In other words, find your DF in the left most column, and follow that row to the right until you locate a value closest to your X² value.
5. Once your X² value is found, follow that column to the very top row to find your p-value, which will reveal the statistical significance.

Okay! Using our info DF=3 and SX²=55.02

1.Find 3 in the leftmost column

2.Follow the row that 3 is in until you find a value closest to 55.02, which on the table is the greatest value the table has to offer of 12.838

3.follow the column that has 12.838 to the top row, which gives us 0.005. Our p-value is 0.005

4.We need to remember when a p-value is significant vs not significant

1. a p-value less than 0.05 is considered statistically significant
2. a p-value greater than 0.05 is considered statistically non-significant

Since 55.02 is much greater than 12.838, the p-value would be even smaller than 0.005

Regardless, 0.005 is less than 0.05, and therefore the data is significant.