Testing%20hypothesis%20with%20two%20proportions%20and%20Chi-square%20testing - PowerPoint PPT Presentation

About This Presentation
Title:

Testing%20hypothesis%20with%20two%20proportions%20and%20Chi-square%20testing

Description:

Testing hypothesis with two proportions and Chi-square testing ... The chi-square test can also be used to test for goodness-of-fit. Goodness of fit ... – PowerPoint PPT presentation

Number of Views:155
Avg rating:3.0/5.0
Slides: 11
Provided by: simmo2
Learn more at: http://people.uncw.edu
Category:

less

Transcript and Presenter's Notes

Title: Testing%20hypothesis%20with%20two%20proportions%20and%20Chi-square%20testing


1
Testing hypothesis with two proportions and
Chi-square testing
2
Hypothesis testing for homogeneity of proportions
  • We wish to compare the effects of two different
    insecticides. The first insectide, InsectsRUs,
    was applied to 300 insects and 50 of them died.
    The second insecticide, InsectsBGone, was applied
    to 350 insects and 90 died. Test to see if there
    is a significant difference in the proportion of
    insects killed.
  • Hypothesis of interest
  • H0 p1 p2 versus HA p1?p2
  • Test statistic
  • Where

3
Calculations
  • InsectsRUs
  • InsectsBGone
  • p-value0.00515

4
Contingency Table
  • Can also view this as a contingency table
  • Type of Insecticide
  • InsectsRUs InsectsBGone
  • Killed 50 90
  • Not killed 250 260
  • TOTAL 300 350

5
Chi-square
  • Chi-square testing can be used to test if the
    distribution is the same in each group (i.e.
    insecticides)
  • Need to find Expected values

6
Expected Values for Chi Square
  • Expected value
  • (row total)(column total)/N

Insects RUs InsectsBGone TOTAL
Killed 50 90 140
Not Killed 250 260 510
TOTAL 300 350 650
Row Totals
Column Totals
N
7
InsectsRUs InsectsBGone TOTAL
Killed 50 90 140
Not Killed 250 260 510
TOTAL 300 350 650
Calculating Expected Values
InsectsRUs InsectsBGone TOTAL
Killed 140300/650 140350/650 140
Not Killed 510300/650 350510/650 510
TOTAL 300 350 650
8
Calculated expected values
InsectsRUs InsectsBGone TOTAL
Killed 64.61538 75.38462 140
Not Killed 235.38462 274.61538 510
TOTAL 300 350 650
Now calculate the Chi square statistic
7.824768 , degrees of freedom 1 p-value
0.00515
9
Comments on the Chi-square Test
  • The test of H0 no association versus HA there
    is an association between two categorical
    variables is computationally the same as testing
    if the conditional distributions are the same
    (this can be extended to more than two
    populations).
  • The degrees of freedom for a chi-square test is
    (r-1)(c-1), where r rows and c columns.
  • Be cautious when expected frequencies are lower
    than 5.
  • The chi-square test can also be used to test for
    goodness-of-fit.

10
Goodness of fit
  • Test to see if percent of longleaf pine is evenly
    distributed across the four quadrants (example
    from Moore, McCabe, and Craig).
  • Quad1 Quad2 Quad3 Quad4
  • Count 18 22 39 21
  • There are a total of 100 trees, so we would
    expect ¼ of 100 to be in each quadrant (where
    expected value 0.2510025).

10.8, degrees of freedom3 P-value0.012858
Write a Comment
User Comments (0)
About PowerShow.com