PSYC 2040 Chapter Notes - Chapter 8: Chi-Squared Test, Chi-Squared Distribution
SchoolUniversity of Guelph
Course CodePSYC 2040
ProfessorNaseem Al- Aidroos
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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
•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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