1 / 12

120 likes | 290 Vues

Chi-Square Test. Mon, Apr 19 th , 2004. Chi-Square ( 2 ). Are 2 categorical variables related (correlated) or independent of each other? Compares # in categories that would be expected by chance (E) to # in categories actually observed (O)

Télécharger la présentation
## Chi-Square Test

**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.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Chi-Square Test**Mon, Apr 19th, 2004**Chi-Square (2)**• Are 2 categorical variables related (correlated) or independent of each other? • Compares # in categories that would be expected by chance (E) to # in categories actually observed (O) • Null hyp (Ho) – no relationship between 2 variables (they’re independent of ea.other) • Alternate (Ha) – the 2 variables are related (not independent)**2 Formula**• 2 = [(fo – fe)2] fe So we’ll compare observed and expected frequencies for each cell in the table…**Is age (<30 v. >30) related to preference for analog/digital**watches? Example**Step 1: Compute Marginals**Marginals are the row and column totals: 140 60 100 20 80**Step 2: Compute Expected Frequencies (fE)**• fE = (Column marginal * Row marginal ) / N For people under 30: fe (digital) = 100 * 140 / 200 = 70 fe (analog) = 80*140 / 200 = 56 fe (undec) = 20*140 / 200 = 14 Over 30: fe (digital) = 100*60 / 200 = 30 fe (analog) = 80*60 / 200 = 24 fe (undec) = 20*60 / 200 = 6**Step 3: Compute X2**• Find difference (residual) betw observed & expected for each cell (fo – fe) • Square those differences • Divide squared differences by fe • Sum the results**(cont.)**• Last step: Add up (fo-fe)2 / fe • 2 = 5.71 + 4.57 + 1.14 + 13.33 + 10.67 + 2.67 = 38.09 • Step 4: Compare to 2 critical with df = (# columns – 1) (# rows – 1) • Here df = (2-1)(3-1) = 2 df, = .05, critical = 5.99**Hypothesis Test**• If 2 observed > 2 critical, reject Ho • Reject Ho conclude there is a relationship between the 2 variables • Here, 38.09 > 5.99, reject Ho, there is a relationship between age & watch preference**In SPSS**• Analyze Descriptive Stats Crosstabs • Choose whichever variable you’d like for ‘row variable’ and the other for ‘column variable’ • Click “Statistics” button, and check chi-squared option • Click “Cells” Button, choose “expected count”**SPSS (cont.)**• Output – look for “Pearson chi-sq” and “Asymp Sig” column gives significance value for chi-sq test: • If “Asymp Sig” value is < .05 (alpha), reject Ho • Note there is an option for clustered graphing, read this example in the lab

More Related