1 / 13

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!”

ronia
Télécharger la présentation

The Chi square hypothesis test

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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?

More Related