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Goodness of fit: How to decide which ratio to deal with?

Goodness of fit: How to decide which ratio to deal with?


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While solving problems of Goodness of fit, I'm faced with an issue, how to decide which ratio to consider to find the test statistic from given set of observations.

E.g. 1

A supplied sample contains four types of seeds and the total number is 64. The types of seeds are large red 42, large white 8, small red 10 and small white 4. Calculate goodness of fit.

Problem: As df=3, Ratio= 9:3:3:1 / 1:1:1:1?

E.g.2

You are supplied with two different varieties of plant samples;tall-76 and short-24. Determine the observed number, apply Chi square test to state whether it is in agreement with expected ratio.

Problem: As df=1, Ratio= 3:1 /1:1?

I was vaguely told by my propessor that which ever ratio seems to apply(by logical guess) we should choose that one to determine the expected values and thus the statistic.

I couldn't find any good read in this regard, except those that are full of mistakes. I've been reading Statistics blogs to understand the concepts but they don't cover these typical biological problems and those that did had the ratios mentioned.

I've another question in mind, from experimental result it is also likely that we won't get one of the four types of seeds (given that mating is random and the progenies appeared by dihybrid crosses) so determining the actual ratio behind becomes more difficult as df = 2 =/= 3!


To solve this question you need to have a basic understanding of Mendelian genetics. Contrary to peoples' comments, this problem does provide enough information.

Genes are inherited from two parents. That is, the offspring will inherit one allele from each parent. Genes also interact with each other in a dominant/recessive nature. A dominant trait will be expressed, no matter what if this is carried by an organism. A recessive trait will only be expressed if the organism is carrying two copies of the same allele - the organism must receive the recessive gene from both parents.

In the first question, there are four genes. One gene encoding large seeds. One gene encoding small seeds. On gene encoding red seeds. One gene encoding white seeds.

The dominant genes are those that code for: large & red The recessive genes are those that code for: small & white

For this question, you assume that both parents are carrying a single copy of each gene. This means, each parent has one copy of a gene coding for large seeds, one copy of a gene coding for small seeds, one copy of a gene coding for red seeds, and one copy of a gene coding for white seeds.

As a side note, this would mean that each parent came from a large red seed. There is also a chance for any of the four genes to be passed to the offspring.

Each parent could pass the genes for: Large red seeds, Large white seeds, small red seeds or small white seeds.

This means that the following gene-combinations are possible:

-large red, large red

-large red, large white

-large red, small red

-large red, small white

-large white, large red

-large white, large white

etc

And, I'm sorry, I've been trying for twenty minutes to upload a picture to show you what I mean. But, you can do this yourself also to see what I mean:

Draw a 4x4 grid, and in each box fill in each possible combination of genes that can be inherited by an offspring. They call this a Punnett square, and it is used to predict the phenotype of an offspring bred by two parents. If you search Punett square you will understand how this works.

But the thing to remember is this: If the offspring carries one copy of a dominate gene (large seed, red seed) then these phenotypes will be expressed. In order for a recessive trait to be expressed, the offspring must carry two copies of the genes (small seed, white seed), ie. it must have received the same recesssive allele from both parents.

Now, to solve the problem statistically, you will use the ratio 9:3:3:1. The null hypothesis is that there is no difference between the observation and this ratio. The alternative hypothesis is that there is a statistically significant difference observed from the sample in comparison to the test-ratio.

This means, a p-value < 0.05 indicates that the 9:3:3:1 ratio is false. And the gene-interaction must be explained by another means - not by Mendelian inheritance. Or, I suppose it could also indicate that the parents did not in fact carry one copy of each allele and some other combination, that maybe you need to find. Eg. One parent could have had two copies of each recessive trait, while the other parent could have had in had one copy of each trait. (Play with the Punnett square, and maybe you can figure out if this is true)


Watch the video: Pearsons chi square test goodness of fit. Probability and Statistics. Khan Academy (May 2022).


Comments:

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