# Segment 16...Multiple Hypotheses

#### Class Activity

w Andrea, Eleisha, Sanmit

1. Data: a number of females n of a pride of lions with N lions

Test statistic: X=n, binomial **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P(n) = \binom{N}{n}p^N(1-p)^{N-n}}**

Null: ratio is 50/50, ie binomial with **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p=.5}**

test using the CDF(n)

2. Data: k is the number of times you had to play until you won

Test statistic: X=k, geometric, **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P(k)=p(1-p)^{k-1}}**

Null: **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p=1/3}**

test using the CDF(k)

3. Data: a set of deviations from the actual point at 0 (a set of distances from the correct location in a one-dimensional world)

Test statistic: X=mean over our data, Gaussian

Null: That **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X=0}**

test using the CDF(N)

4. Data: multiple times that we sample (to failure of the stoplights)

Test statistic: X=mean time over the N times that we sampled it.

Null: With exponential distribution, the mean is **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X=\text{quoted time}}**

test using the CDF(X)

Bonf: For this correction, we need a new threshold for significance for test multiple hypothesis. Our new threshold is 0.05/N, where N is the sum of the number of ORFs obtained for each frame. This number was obtained by taking all of the p values and putting them in an array. We then just took the length of that array to calculate N. Lastly we used this new threshold to find the number of significant p-values in our array.