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# Chi-square Basics - PowerPoint PPT Presentation

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

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### Chi-square Basics

• 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) =

• 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.

• 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?

• Reject H0

• The district will probably vote democratic

• However…

• 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

• What do stats kids do with their free time?

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

• R = number of rows

• C = number of columns

Interpretation kids do with their free time?

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

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 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 kids do with their free time?

• Contingency coefficient

• Phi

• Cramer’s Phi

• Odds Ratios

• Kappa

• These were discussed in 5700