School

University of GuelphDepartment

PsychologyCourse Code

PSYC 2040Professor

Naseem Al- AidroosChapter

8This

**preview**shows page 1. to view the full**4 pages of the document.**ch 8- chi square (summary)

•chi square testing is used when determining differences in frequency of events

•tries to find an association/ contingency/ correlation between factors of interest

•compares the expected frequencies with obtained frequencies and determines the

goodness of fit of the data to the model

←-ex: the frequency of smoking vs non- smoking and the relation between gender

•X2 (chi-square) statistic:

•O = the obtained frequency

•E = the expected frequency

•the sampling distribution is approximated by the density function for X2

➡with degrees of freedom equal to the number of obtained frequencies that are free to

vary given whatever restrictions imposed provided that the null hypothesis is true.

•null hypothesis: that in the population the observed frequencies equal the expected frequencies.

➡expect a given amount of variability based on sampling

➡if this variability is greater than what would be expected on the basis of chance, then

one would conclude that the null hypothesis is not true

•this is evaluated using the T distribution or the F-distribution.

•With 1 degree of freedom, the

distribution is exponential

•df 5- shows as an

asymmetrical distribution with

a long tail running to the right

•df-10, the distribution is

somewhat less skewed, but

nonetheless asymmetrical.

•the mean of the chi-square

distribution increases (the

centre of the distribution

moves to the right) as the

degrees of freedom increase.

•as df increases, the value required for significance also increases.

•For 1 df, a value of 3.84 is required for significance at the .05 level, and a value of 6.84 is

required at the .01 level.

•the X2 statistic is not a parametric distribution

➡it’s the ratio of the sum of squared deviations of n observations from their sample mean

divided by the population variance.

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