Chi square basics
Download
1 / 15

- PowerPoint PPT Presentation


  • 431 Views
  • Updated On :

Chi-square Basics. The Chi-square distribution. Positively skewed but becomes symmetrical with increasing degrees of freedom Mean = k where k = degrees of freedom Variance = 2k Assuming a normally distributed dataset and sampling a single z 2 value at a time  2 (1) = z 2

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '' - Faraday


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

The chi square distribution l.jpg
The Chi-square distribution

  • Positively skewed but becomes symmetrical with increasing degrees of freedom

  • Mean = k where k = degrees of freedom

  • Variance = 2k

  • Assuming a normally distributed dataset and sampling a single z2 value at a time

    • 2(1) = z2

    • If more than one… 2(N) =


Why used l.jpg
Why used?

  • Chi-square analysis is primarily used to deal with categorical (frequency) data

  • We measure the “goodness of fit” between our observed outcome and the expected outcome for some variable

  • With two variables, we test in particular whether they are independent of one another using the same basic approach.


One dimensional l.jpg
One-dimensional

  • Suppose we want to know how people in a particular area will vote in general and go around asking them.

  • How will we go about seeing what’s really going on?


Slide5 l.jpg



Slide7 l.jpg

  • Reject H0

  • The district will probably vote democratic

  • However…


Conclusion l.jpg
Conclusion

  • Note that all we really can conclude is that our data is different from the expected outcome given a situation

    • Although it would appear that the district will vote democratic, really we can only conclude they were not responding by chance

    • Regardless of the position of the frequencies we’d have come up with the same result

    • In other words, it is a non-directional test regardless of the prediction


More complex l.jpg
More complex

  • What do stats kids do with their free time?


Slide10 l.jpg


Slide11 l.jpg

  • df = (R-1)(C-1) kids do with their free time?

    • R = number of rows

    • C = number of columns


Interpretation l.jpg
Interpretation kids do with their free time?

  • Reject H0, there is some relationship between gender and how stats students spend their free time


Other l.jpg
Other kids do with their free time?

  • Important point about the non-directional nature of the test, the chi-square test by itself cannot speak to specific hypotheses about the way the results would come out

  • Not useful for ordinal data because of this


Assumptions l.jpg
Assumptions kids do with their free time?

  • Normality

    • Rule of thumb is that we need at least 5 for our expected frequencies value

  • Inclusion of non-occurences

    • Must include all responses, not just those positive ones

  • Independence

    • Not that the variables are independent or related (that’s what the test can be used for), but rather as with our t-tests, the observations (data points) don’t have any bearing on one another.

  • To help with the last two, make sure that your N equals the total number of people who responded


Measures of association l.jpg
Measures of Association kids do with their free time?

  • Contingency coefficient

  • Phi

  • Cramer’s Phi

  • Odds Ratios

  • Kappa

  • These were discussed in 5700


ad