You have exposed some algae to a highsalinity environment and used highthroughput sequencing to measure gene expression levels. You have a list of 50 genes that are known to be involved in helping cells respond to high salinity and want to know whether more of those genes show a change in their expression (i.e., are either upregulated or downregulated). To do so, you can compare the observed number of upregulated genes from that list to the number that might be expected.
Number observed 
Number Expected 
Chisquare statistic 

Increase in expression 
15 
16.67 

No change in expression 
15 
16.67 

Decrease in expression 
20 
16.67 
1
onsider a case where you expect the 50 genes to be equally likely to increase, decrease, or show no change in their expression levels. Calculate the chisquare statistics for each set of genes and enter it below.
Number observed 
Number Expected 
Chisquare statistic 

Increase in expression 
15 
16.67 
Answer 
No change in expression 
15 
16.67 
Answer 
Decrease in expression 
20 
16.67 
Answer 
2What is the overall chisquared statistic?
3How many degrees of freedom are there?
4Calculate the probability of the chisquared statistic to 2 decimal places & would you reject the null hypothesis that these observed counts are no different from expected? Explain why in one or two sentences.
Answer(1):
H_{0}: observed counts are no different from expected
H_{1}: observed counts are significantly different from expected
Number observed 
Number Expected 
Chisquare statistic=(oe)^{2}/e 

Increase in expression 
15 
16.67 
0.16730054 
No change in expression 
15 
16.67 
0.16730054 
Decrease in expression 
20 
16.67 
0.66520096 
Answer(2):
The overall statistic can be obtained by adding the individual statistic
Answer(3):
We have total 3 observations, i.e. n=3
Hence the degrees of freedom =n1 = 31 = 2
Answer(4): The pvalue for above test is 0.61
The pvalue is greater than α=0.05 which indicates that we do not have enough evidence against null hypothesis to reject it, so we fail to reject the null hypothesis and we can conclude that these observed counts are no different from expected.
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