Chapter 11 Chi Square Distribution and goodness of fit

1
Chapter 11Chi Square Distributionand goodness
of fit
2
What is Goodness of Fit?

• This application is a way to evaluate whether
  population fits a distribution.
• How closely does observed data match an idealized
  situation?

3
?2 Goodness of Fit (cont)

• Why right tailed?
• For both ?2 tests, the idea is to see if the
  measure between the observed and expected
  frequencies is too large (i.e. to the right) to
  be due to chance alone.

4
Do we still have hypotheses?

• Why yes, we do.
• HO Population fits the given distribution
• HA Population does not fit the given
  distribution
• It will look VERY similar with just one small
  change

5
?2 Goodness of Fit (cont)
d.f. k 1 where k number of categories in
the distribution
6
Births Sign
23 Aries
20 Taurus
18 Gemini
23 Cancer
20 Leo
19 Virgo
18 Libra
21 Scorpio
19 Sagittarius
22 Capricorn
24 Aquarius
29 Pisces

• The table to the right is the zodiac signs of 256
  heads of the largest 400 companies.
• The natural null would be that the birth dates
  are divided equally among all the signs of the
  zodiac. Compute the test statistic to evaluate
  how closely the observed data matches this
  idealized situation.

7

• 1. Compute the null and alternate hypotheses.
• 2. Check the conditions
• 3. Compute ?2.
• 4. Find the degrees of freedom.
• 5. Conclude

Births Sign
23 Aries
20 Taurus
18 Gemini
23 Cancer
20 Leo
19 Virgo
18 Libra
21 Scorpio
19 Sagittarius
22 Capricorn
24 Aquarius
29 Pisces
8
The difference?

• The previous lesson was using ?2 to evaluate
  independence.
• This lesson uses ?2 to see how well data fits
  expected models.