Our first hypothesis test - Student's t-test

Performing Experiments in Python

Luke Hayden

Instructor

From observed pattern to reliable result

Data contains patterns

Some expected
Others surprising
Random variation also

Dealing with this

How do we go from observation to result?

Are these groups different?

Weights of two groups of adults

Sample A:

[66.1, 69.8,67.7,69.6,71.1]

Sample B:

[83.7,81.5, 80.6, 83.9, 84.4]

(p9.ggplot(df)+ 
p9.aes('Value', fill='Sample')+ 
p9.geom_density(alpha=0.5))

Are these different?

Two hypotheses

Null hypothesis

A = B

Observed patterns are the product of random chance

Alternative hypothesis

A != B

Difference between samples represents a real difference between the populations

A density plot of a bimodal distribution

Some statistical terms

p-value

Likelihood of pattern under null hypothesis

alpha

Crucial threshold of p-value
Usually alpha < 0.05: reject null hypothesis

Student's t-test

Invented by William Sealy Gosset
Two basic types:

One-sample: Mean of population different from a given value?

Two-sample: Two means equal?

Coding a t-test

from scipy import stats 


stats.ttest_ind(Sample_A, Sample_B)

Implementing a one-sample t-test

from scipy import stats 

Sample_A = df[df.Sample == "A"] 

t_result = stats.ttest_1sample(Sample_A, 65)

alpha = 0.05

if (t_result[1] < alpha):
    print("mean(A) != 65")

mean(A) != 65

Implementing a two-sample t-test

from scipy import stats 

Sample_A = df[df.Sample == "A"] 
Sample_B = df[df.Sample == "B"] 

t_result = stats.ttest_ind(Sample_A, Sample_B)

alpha = 0.05

if (t_result[1] < alpha):
    print("A and B are different!")

A and B are different!

Now let's try it out!

Performing Experiments in Python