Hypothesis testing

Hypothesis testing

1. things to know

   • Graph representations
   • Steps for Hypothesis testing
     • 1) Choose the null and alternative hypotheses
       • Null Hypothesis (Ho)
         • a population parameter
         • a statement
         • being equal to some value
       • Alternative Hypothesis (H1)
         • contrary to null hypothesis
     • 2) Choose a significance level
       • α
         • probability rejecting Ho (α = P (reject Ho| Ho true))
     • 3) Calculate the test statistics
       • z / t / x2
         • Test statistic = (point estimate - null value) / Standard Error
           • ...
     • 4) Calculate the p value
       • the area under the sampling distribution
       • P(the observed sample outcome|H_0 true) = P(X>c| H_0 true), c = critical value
       • extreme in the direction of the alternative hypothesis
     • 5) State a conclusion
       • If p-value < α, reject null hypothesis
       • If p-value > α, do not reject null hypothesis

2. types of test

   • t - test
     • Degrees of freedom: n - 1
     • for one mean
     • for two means
       • paired data: taking data twice
       • unpaired data: taking data from different groups
       • watch pooled/not pooled
         • S1 and S2 are similar, and if S1 (the biggest one) < 2 · S2 then it's pooled
   • type I error
     • the test result says you have coronavirus, but you actually don’t (false positive)
       • P (reject Ho|Ho true)
   • type II error
     • the test result says you don’t have coronavirus, but you actually do (false negative)
       • P (accept Ho | Ho false)
   • Chi squared goodness of fit
     • • The data is from a multinomial experiment. • All expected values are at least 5. (Another rule of thumb is that there are more than 4 groups, the average of the expected values is at least 5, and the smallest expected value is at least 1.)
     • to see of the data fits a distribution
     • degrees of freedom: k - 1 , k= the number of groups or cells in the contingency table.
   • Chi-squared test for independence / Goodness of fit
     • • The data is multinomial data in a contingency table or two way cross-classification table. • All expected values are at least 5. (Another rule of thumb is that there are more than 4 cells, the average of the expected values is at least 5, and the smallest expected value is at least 1.) • The cells have counts or frequencies. It doesn't work if the data is percentages or relative frequencies! • The data comes from one population.
     • degrees of freedom: df = (rows − 1) (columns − 1)
     • used to see if two variables are independent.
   • z - test

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