Chi Square. What does Chi-square analysis tell us ? If the difference between your observed results...
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Transcript of Chi Square. What does Chi-square analysis tell us ? If the difference between your observed results...
Chi Square
What does Chi-square analysis tell us?
If the difference between your observed results and expected results are due to random chance or not.
EX –flip a coin enough and you would expect to get heads 50% of time and tails 50% of time. If this number is way off even after 1,000 tosses then something else besides randomness is occurring
How’s it works
Calculation to use is
X2 = ∑ (observed – expected)2
expected
Table to set up# of Possible
Outcomes
Observed Expected X2
How it works continued
• Determine degrees of freedom – it’s one less than the number of possible outcomes
Ex – expect 4 different phenotypes, degrees of freedom is 3
Ex 2 – expect a cell to be in one of two different phases, degrees of freedom is ___
What are you looking for? Support for or against the null hypothesis.
• Null Hypothesis= there will be no difference between observed and expected results
• p = .05 is the cut off pt for most scienitific data, you’re asking does the data support my NULL hypothesis?
• Ex. Is the variable being tested actually making a significant difference? We start by assuming it won’t.
How it works
• Once you have your degrees of freedom and Chi square answer, go to the distribution table and compare your answer to the critical value in the 0.05 column
What?
• If X2 answer is lower than critical value – ACCEPT the null hypothesis
• If X2 answer is higher than critical value – REJECT the null hypothesis (something is going on other than randomness)
REJECT NULLACCEPT NULL
Explain please
• If p = .05 then what does that mean?
the difference between observed and expected results is due to random events 5% of time if your critical factor is equal to or less.
Your NULL hypothesis is supported! (if higher than critical factor than NULL
hypothesis not supported – something going on)
Try it
• P = Purple • p = Yellow • S = Smooth PpSs x PpSs• s = Shrunken
What are the expected results? Hypothesis? 9:3:3:1 due to independent
assort of alleles
Results analysis
• Observed results: An ear of corn has a total of 381 grains, including 216 Purple & Smooth, 79 Purple & Shrunken, 65 Yellow & Smooth, and 21 Yellow & Shrunken.
• Expected? – do the dihybrid p-square if need to
Table, Chi Square and Degrees of Freedom
Possible Outcomes
Observed Expected Chi Square
X2 = ∑ (observed – expected)2
expected
Purple/
smooth
216
Purple/ shrunken
79
Yellow/ smooth
65
Yellow/ shrunken
21
SUM of Chi Squares: Df:
Hypothesis supported?
• 2.197 is chi square value – compare to proper critical value
Answer
• 2.197 is less than critical value of 7.82 therefore……
• Null hypothesis is ACCEPTED – there is no significant difference between observed data and expected!!!
Try this one
• Same hypothesis: independent assort therefore 9:3:3:1 outcome is expected
• Observed: An ear of corn has a total of 389 grains, including 219 Purple & Smooth, 70 Yellow & Smooth, and 100 white.
Possible Outcomes
Observed Expected Chi Square
X2 = ∑ (observed – expected)2
expected
Purple/
smooth
Purple/ shrunken
Yellow/ smooth
Yellow/ shrunken
Mitosis Lab
• State a null hypothesis for the experimental treatment on mitosis rate for onion root tip:
• How will we collect data for the Expected results?
• How will we collect data for the Observed results?
• Hint – keep it simple, the cell is either in_______ or _________.
• Helpful video: Bozeman Chi Square
Practice makes perfect
• Animal Behavior data from the Bozeman Video
• Next few slides: Mendelian genetics practice
6. FRUIT FLY GENETICS
Cross two heterozygous wild type fruit flies for the traits below. Predict expected outcomes of offspring using a punnett square. W= normal wings w=vestigial
B = normal body b = black
Go to the next slide for actual results then perform Chi Square to determine if there is a significant statistical difference between the expected and observed results.
Actual results of the cross
800 Wild/Wild
55 wild-type wings/ black body
50 vestigial wings/ wild type body
902 vestigial/ black body