Chi Square Analysis

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Chi Square Analysis

• The chi square analysis allows you to use
  statistics to determine if your data good or
  not.
• In our fruit fly labs we are using laws of
  probability to determine possible outcomes for
  genetic crosses.
• How will we know if our fruit fly data is good?

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m m

• Peanut mm data from Mars
• Peanut butter mm data from Mars

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• The following formula is used

• If your hypothesis is supported by data
• you are claiming that mating is random and so is
  segregation and independent assortment.
• If your hypothesis is not supported by data
• you are seeing that the deviation between
  observed and expected is very far apartsomething
  non-random must be occurring.

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• The test statistic is compared to a theoretical
  probability distribution
• In order to use this distribution properly you
  need to determine the degrees of freedom
• Degrees of freedom is the number of phenotypic
  possibilities in your cross minus one.
• If the level of significance read from the table
  is greater than .05 or 5 then your hypothesis is
  accepted and the data is useful

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• The hypothesis is termed the null hypothesis
  which states that there is no substantial
  statistical deviation between observed and
  expected data.

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Lets look at a fruit fly cross
x
Black body, eyeless
wild
F1 all wild
7
F1 x F1
5610
1881
622
1896
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Analysis of the results

• Once the numbers are in, you have to determine
  the cross that you were using.
• What is the expected outcome of this cross?
• 9/16 wild type 3/16 normal body eyeless 3/16
  black body wild eyes 1/16 black body eyeless.

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Now Conduct the Analysis
To compute the hypothesis value take 10009/16
626
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Now Conduct the Analysis
To compute the hypothesis value take 10009/16
626
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• Using the chi square formula compute the chi
  square total for this cross
• (5610 - 5630)2/ 5630 .07
• (1881 - 1877)2/ 1877 .01
• (1896 - 1877 )2/ 1877 .20
• (622 - 626) 2/ 626 .02
• ? 2 .30
• How many degrees of freedom?

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• Using the chi square formula compute the chi
  square total for this cross
• (5610 - 5630)2/ 5630 .07
• (1881 - 1877)2/ 1877 .01
• (1896 - 1877 )2/ 1877 .20
• (622 - 626) 2/ 626 .02
• ? 2 .30
• How many degrees of freedom? 3

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CHI-SQUARE DISTRIBUTION TABLE
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• When reporting chi square data use the following
  formula sentence.
• With degrees of freedom, my chi square value
  is , which gives me a p value between and
  , I therefore my null hypothesis.
• This sentence would go in the reults section of
  your formal lab.
• Your explanation of the significance of this data
  would go in the discussion section of the
  formal lab.

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• Looking this statistic up on the chi square
  distribution table tells us the following
• the P value read off the table places our chi
  square number of .30 close to .95 or 95
• This means that 95 of the time when our observed
  data is this close to our expected data, this
  deviation is due to random chance.
• We therefore accept our null hypothesis.

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• What is the critical value at which we would
  reject the null hypothesis?
• For three degrees of freedom this value for our
  chi square is gt 7.815
• What if our chi square value was 8.0 with 4
  degrees of freedom, do we accept or reject the
  null hypothesis?
• Accept, since the critical value is gt9.48 with 4
  degrees of freedom.

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• How can we use the chi square test in a different
  sort of lab?
• If we were testing the effect of light on plant
  growth, how could the chi square analysis be
  used?
• In this case our experimental group is plants
  grown in the dark and the control plants are
  grown in the light.

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• What would your expected data be?
• Control plants grown in the light.
• What would your observed group be?
• Plants grown in the dark.
• Do you expect to accept or reject the null
  hypothesis?
• reject