Chisquare Test

1
Chi-square Test

• also called chi-squared or ?2  distribution

2

• In statistics, a result is significant if it is
  unlikely to have occurred by chance.
• Because maybe youre not being a great scientist
  and the independent variable (the test condition
  being examined) has no effect. Maybe you got
  results by chance.

3
Null hypothesis

• In statistics, a null hypothesis is a hypothesis
  set up to be nullified or refuted in order to
  support an alternative hypothesis. When used, the
  null hypothesis is presumed true until
  statistical evidence in the form of a hypothesis
  test indicates otherwise.

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• So when you do a Chi-Square test you say I have
  a null hypothesis that I got this result in my
  experiment because of chance Now you dont
  really think that. You are setting out to reject
  the null hypothesis so you can accept your
  alternative hypothesis. Your alternative
  hypothesis would be something like, This
  experimental result is NOT because of chance it
  is because of the variables I set up. I am a
  genius.

5

• The significance of a result is also called its
  p-value
• the smaller the p-value, the more significant the
  result is said to be.
• We say that if the p-value is low enough that we
  reject the null hypothesis and accept the
  alternative hypothesis.
• it wasnt chance, it was the thing in my
  experiment

6

• Popular levels of significance are 10, 5, and
  1 , all represented by the Greek symbol, a
  (alpha). Remember you could write those as 0.10
  0.05 and 0.01
• We use 5 a lot
• If the p-value is lower than 0.05 you can say
  there is less than a 5 possibility that this was
  chance. It was probably this other thing

7

• Maybe its chance that so people who smoke
  cigarettes get lung cancer.
• If you do a chi-square test and get a p-value of
  0.01 it means that its only 1 likely that its
  chance. Its the alternative hypothesis that
  cigarettes are causing lung cancer.

8

• Note that when there are only 2 categories there
  are some mathematical problems with this test,
  but variations exist to fix that.
• Chi-square tests accepts weak or less accurate
  data and there are stricter statistical tests
• However sometimes you can only get weak or
  slightly fuzzy data like when looking at tens of
  thousands of cases of lung cancer, those people
  lead pretty different lives.