1 / 57

570 likes | 733 Views

Chi-square = 2.85 Chi-square crit = 5.99 Achievement is unrelated to whether or not a child attended preschool. 2 as a test for goodness of fit. So far. . . . The expected frequencies that we have calculated come from the data They test rather or not two variables are related.

Download Presentation
## Chi-square = 2.85 Chi-square crit = 5.99

**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 = 2.85**• Chi-square crit = 5.99 • Achievement is unrelated to whether or not a child attended preschool.**2 as a test for goodness of fit**• So far. . . . • The expected frequencies that we have calculated come from the data • They test rather or not two variables are related**2 as a test for goodness of fit**• But what if: • You have a theory or hypothesis that the frequencies should occur in a particular manner?**Example**• M&Ms claim that of their candies: • 30% are brown • 20% are red • 20% are yellow • 10% are blue • 10% are orange • 10% are green**Example**• Based on genetic theory you hypothesize that in the population: • 45% have brown eyes • 35% have blue eyes • 20% have another eye color**To solve you use the same basic steps as before (slightly**different order) • 1) State the hypothesis • 2) Find 2 critical • 3) Create data table • 4) Calculate the expected frequencies • 5) Calculate 2 • 6) Decision • 7) Put answer into words**Example**• M&Ms claim that of their candies: • 30% are brown • 20% are red • 20% are yellow • 10% are blue • 10% are orange • 10% are green**Example**• Four 1-pound bags of plain M&Ms are purchased • Each M&Ms is counted and categorized according to its color • Question: Is M&Ms “theory” about the colors of M&Ms correct?**Step 1: State the Hypothesis**• H0: The data do fit the model • i.e., the observed data does agree with M&M’s theory • H1: The data do not fit the model • i.e., the observed data does not agree with M&M’s theory • NOTE: These are backwards from what you have done before**Step 2: Find 2 critical**• df = number of categories - 1**Step 2: Find 2 critical**• df = number of categories - 1 • df = 6 - 1 = 5 • = .05 • 2 critical = 11.07**Step 3: Create the data table**Add the expected proportion of each category**Step 4: Calculate the Expected Frequencies**Expected Frequency = (proportion)(N)**Step 4: Calculate the Expected Frequencies**Expected Frequency = (.30)(2081) = 624.30**Step 4: Calculate the Expected Frequencies**Expected Frequency = (.20)(2081) = 416.20**Step 4: Calculate the Expected Frequencies**Expected Frequency = (.20)(2081) = 416.20**Step 4: Calculate the Expected Frequencies**Expected Frequency = (.10)(2081) = 208.10**Step 5: Calculate 2**O = observed frequency E = expected frequency**2**15.52**Step 6: Decision**• Thus, if 2 > than 2critical • Reject H0, and accept H1 • If 2 < or = to 2critical • Fail to reject H0**Step 6: Decision**2 = 15.52 2 crit = 11.07 • Thus, if 2 > than 2critical • Reject H0, and accept H1 • If 2 < or = to 2critical • Fail to reject H0**Step 7: Put answer into words**• H1: The data do not fit the model • M&M’s color “theory” did not significantly (.05) fit the data**Practice**• Among women in the general population under the age of 40: • 60% are married • 23% are single • 4% are separated • 12% are divorced • 1% are widowed**Practice**• You sample 200 female executives under the age of 40 • Question: Is marital status distributed the same way in the population of female executives as in the general population ( = .05)?**Step 1: State the Hypothesis**• H0: The data do fit the model • i.e., marital status is distributed the same way in the population of female executives as in the general population • H1: The data do not fit the model • i.e., marital status is not distributed the same way in the population of female executives as in the general population**Step 2: Find 2 critical**• df = number of categories - 1**Step 2: Find 2 critical**• df = number of categories - 1 • df = 5 - 1 = 4 • = .05 • 2 critical = 9.49**Step 5: Calculate 2**O = observed frequency E = expected frequency**2**19.42**Step 6: Decision**• Thus, if 2 > than 2critical • Reject H0, and accept H1 • If 2 < or = to 2critical • Fail to reject H0**Step 6: Decision**2 = 19.42 2 crit = 9.49 • Thus, if 2 > than 2critical • Reject H0, and accept H1 • If 2 < or = to 2critical • Fail to reject H0**Step 7: Put answer into words**• H1: The data do not fit the model • Marital status is not distributed the same way in the population of female executives as in the general population ( = .05)**Practice**• Is there a significant ( = .05) relationship between gender and a persons favorite Thanksgiving “side” dish? • Each participant reported his or her most favorite dish.**Results**Side Dish Gender**Step 1: State the Hypothesis**• H1: There is a relationship between gender and favorite side dish • Gender and favorite side dish are independent of each other

More Related