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The Chi square hypothesis test

The Chi square hypothesis test. Chi squared is a means of Hypothesis testing : χ 2 Chi-squared= = Σ _(O-E) 2 E The Chi Squared test can help make an impartial judgment about data. Example: Form a hypothesis and test it. Hypothesis: “That quarter is loaded!”

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The Chi square hypothesis test

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  1. The Chi square hypothesis test • Chi squared is a means of Hypothesis testing: χ2 • Chi-squared= = Σ_(O-E)2 E The Chi Squared test can help make an impartial judgment about data.

  2. Example: Form a hypothesis and test it • Hypothesis: “That quarter is loaded!” • Test: Toss the coin ten times, and count the number of heads. Compare results to expectations using chi-squared test!

  3. Steps in Chi-Square analysis • 1. Form a null hypothesis (H0) • 2. Calculate Chi-square • 3. Determine degrees of freedom • 4. Decide on minimum acceptable confidence level (usually 95%) • 5. Obtain P-value • 6. Evaluate null hypothesis (reject/ fail to reject)

  4. Steps in chi-square analysis • 1. Form a Null hypothesis: Ho =“ The coin isn’t loaded, and any differences between my results and what I expect are just due to luck.” • A null hypothesis is a hypothesis set up to be nullified. It is created in order to support an alternative hypothesis (“my friend is a scam artist with a loaded coin!”)

  5. Experimental results What do you think?

  6. Step 2: Calculate Chi Squared • Chi-squared can tell you the likelihood your results are just due to chance • What do we expect, according to the null hypothesis? • What did we observe? • (8-5)2/5 + (2-5)2/5 = 18/5 = 3.6= χ2 Σ= sigma= “sum of” Σ(O-E)2/E=sum of (Observed – Expected)2/expected = (8 heads - 5 heads)2 + (2 tails- 5 tails)2/ 5 heads = (9/5) + (9/5) = 3.6

  7. Step 3: Determine degrees of freedom • df = number of possible outcomes-1 • For us: outcome 1: “heads”, outcome 2: “tails” • Therefore 2 possible outcomes – 1= 1= df

  8. Step 4: Decide upon a minimum acceptable level of confidence • How much confidence must we have in our answer? • P = .05: 95% confidence • P = .01: 99% confidence Degrees of freedom = number of boxes – 1 (we have 2 boxes, therefore 1 df) In the boxes: chi-squared values We must have a χ2 value greater than this to reject at 95% confidence

  9. Step 5: Evaluate null hypotheis • So, is the coin loaded? • Since we require a greater than 95% confidence in order to reject our null hypothesis (χ2> 3.84), we cannot reasonably claim the coin is loaded. • Fail to reject Ho!

  10. Your homework • Determine using chi square if the genes in problem 4 of last week’s quiz are linked. • What is our null hypothesis? • What are our observed values? • What are our expected values? • What is our value of chi-squared? • How many possible outcomes are there? • Degrees of freedom? • P-value? • Reject or fail to reject Ho?

  11. Another question: Quiz “Problem 6½” • In a farm in Brno, Czech Republic, Gregor Mendel was doing the same cross, and got the following results: • Parental: 470 + 455 • Recombinant: 35 + 40 You think Gregor Mendel is a sketchy character who doesn’t do his crosses correctly. Did he make a mistake? Did you? Compare his results with yours using chi-square.

  12. Applying the Chi-squared test to your drosophila experiment • Is your gene sex-linked? • Autosomal? • Dominant? • Recessive? • Make a hypothesis: Aldox is dominant! • Make your cross • Count the offspring • What results would you expect if your hypothesis were true?

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