Chi Squared Interpretation Goodness of Fit

1
Chi Squared InterpretationGoodness of Fit

• How well does the hypothesis agree with the data
• How likely is it that the variations that data
  show (from the predicted values) are caused by
  chance occurrences
• Or are the variances really because I have the
  wrong hypothesis.
• gt wrong predictions

2
Goodness of fit?
3
Chi Squared

• Calculate chi squared (?2)
• The ?2 indicates the degree of over all
  deviation.
• The Table shows the probability of this
  occurring by chance
• If there is a high probability of the deviations
  occurring by chance then the predictions might be
  correct.

4

• Higher probability of deviation occurring by
  chance
• small Chi squared
• Lower probability of deviation occurring by
  chance
• large Chi squared

5
Accept or Reject ??
Significance level ( D value ) Decision
If the ?2 value for a particular number of degrees of freedom is found in a column for P 0.05 or less Then the chance of the deviations occurring by chance is too small the hypothesis should be rejected
If the ?2 value for a particular number of degrees of freedom is found in a column for P 0.95 or greater Then the chance of the deviations occurring by chance is very good and the hypothesis should be accepted
If the ?2 value for a particular number of degrees of freedom is found in columns where 0.05 lt P lt 0.95 Then the chance of the deviations occurring by chance is unclear and the hypothesis can not be accepted or rejected. gt repeat the experiment