Choosing the Right Test (Review) Type of test depends on variable types: 1 categorical: z test about population proportion � Lecture 28/Chapters 22 & 23 1 measurement (quan) [pop sd known or sample large]: � z test about mean Hypothesis Tests 1 measurement (quan) [pop sd unknown & sample small]: � t test about mean 1 categorical (2 groups)+ 1 quan: two-sample z or t � � Variable Types and Appropriate Tests 2 categorical variables: chi-square test (done in Chapter 13) � � Choosing the Right Test: Examples � Example: Reviewing Chi-Square � Type I and Type II Error Null and Alternative Hypotheses (Review) Testing Hypotheses About a Population Formulate hypotheses For a test about a single mean, 1. about single proportion or mean or two means o � Null hypothesis: claim that the population mean (alternative can have < or > or � sign) equals a proposed value. about relationship using chi-square: null hyp states o � Alternative hypothesis: claim that the two cat. variables are not related; alt states they are. population mean is greater, less, or not equal to a Summarize/standardize data. 2. proposed value. Determine the P -value. (2-sided is twice 1-sided) 3. An alternative formulated with � is two-sided ; Make a decision about the population: believe 4. with > or < is one-sided . alt if P -value is small; otherwise believe null. For practice, we’ll consider a variety of examples. In each case we’ll formulate appropriate hypotheses and state what type of test should be run.
Example: Smoking and Education (#1 p. 427) Example: Test about Smoking and Education Background : Consider years of education for mothers who Background : Consider years of education for mothers � � smoke compared with those who don’t, in sample of 400 who smoke compared with those who don’t, in sample mothers, to decide if one group tends to be more educated. of 400 mothers, to decide if one group tends to be more Question: Which of the 5 situations applies? � educated. 1. 1 categorical: z test about population proportion Question: What hypotheses and test are appropriate? � 2. 1 measurement (quan) [pop sd known or sample large]: Response: z test about mean � Null: ___________________________________________________ 3. 1 measurement (quan) [pop sd unknown & sample small]: t test about mean Alt: ____________________________________________________ 4. 1 categorical (2 groups) + 1 quan: two-sample z or t Do _______________ [large samples] test to compare ____________ 5. 2 categorical variables: chi-square test Alternative is___________ because no initial suspicion was expressed about a specific group being better educated . Response: _____ � Example: ESP? (Case Study 22.1 p. 425) Example: Test about ESP Background : A subject in an ESP experiment chooses each time Background : A subject in an ESP experiment chooses � � from 4 targets the one which he/she believes is being “sent” by each time from 4 targets the one which he/she believes extrasensory means. Researchers want to determine if the subject is being “sent” by extrasensory means. Researchers performs significantly better than one would by random guessing. want to determine if the subject performs significantly Question: Which of the 5 situations applies? � better than one would by random guessing. 1. 1 categorical: z test about population proportion Question: What hypotheses and test are appropriate? � 2. 1 measurement (quan) [pop sd known or sample large]: Response: z test about mean � 3. 1 measurement (quan) [pop sd unknown & sample small]: Null: population proportion correct _______ t test about mean Alt: population proportion correct ________ 4. 1 categorical (2 groups) + 1 quan: two-sample z or t Do ___ test about _____________________ 5. 2 categorical variables: chi-square test Response: ____ �
Example: Calcium for PMS (#3-4 p. 428) Example: Test about Calcium for PMS Background : We want to compare change in severity of PMS Background : We want to compare change in severity � � symptoms (before minus after, measured quantitatively) for 231 of PMS symptoms (before minus after, measured women taking calcium vs. 235 on placebo to see if calcium helps. quantitatively) for 231 women taking calcium vs. 235 Question: Which of the 5 situations applies? � on placebo to see if calcium helps. 1. 1 categorical: z test about population proportion Question: What hypotheses and test are appropriate? � 2. 1 measurement (quan) [pop sd known or sample large]: Response: z test about mean � Null: mean symptom change (calc)__mean symptom change (placebo) 3. 1 measurement (quan) [pop sd unknown & sample small]: t test about mean Alt: mean symptom change (calc)__mean symptom change (placebo) 4. 1 categorical (2 groups) + 1 quan: two-sample z or t Do _____________ [large samples] test to compare means 5. 2 categorical variables: chi-square test Alternative is__________ because we hope or suspect that the calcium group will show more symptom improvement. Response: ____ � As always, our hypotheses refer to the___________, not the________ Example: Incubators, Claustrophobia (6b p.428) Example: Test about Incubators, Claustrophobia Background : We want to see if placing babies in an Background : We want to see if placing babies in an incubator � � during infancy can lead to claustrophobia in adult life. incubator during infancy can lead to claustrophobia in adult life. Question: Which of the 5 situations applies? � 1. 1 categorical: z test about population proportion Question: What hypotheses and test are appropriate? � 2. 1 measurement (quan) [pop sd known or sample large]: Response: � z test about mean Null: there is___relationship between incubation and claustrophobia 3. 1 measurement (quan) [pop sd unknown & sample small]: Alt: there is___relationship between incubation and claustrophobia t test about mean Do ____________test. 4. 1 categorical (2 groups) + 1 quan: two-sample z or t Alternative is general (2-sided) because __________doesn’t let us 5. 2 categorical variables: chi-square test specify our initial suspicions in a particular direction. Response: ____ �
Example: Training Program, Scores (#7 p.446) Example: Test about Training Program, Scores Background : We want to see if a training program helps raise Background : We want to see if a training program � � students’ scores. For each student, researchers record the helps raise students scores. For each student, increase (or decrease) in the scores, from pre-test to post-test. researchers record the increase (or decrease) in the Question: Which of the 5 situations applies? � scores, from pre-test to post-test. 1. 1 categorical: z test about population proportion Question: What hypotheses and test are appropriate? � 2. 1 measurement (quan) [pop sd known or sample large]: Note: As always, our hypotheses refer Response: z test about mean � to population values. It’s not enough Null: population mean increase___ to simply exhibit an increase in sample 3. 1 measurement (quan) [pop sd unknown & sample small]: scores; the increase must be t test about mean Alt: population mean increase___ statistically significant . 4. 1 categorical (2 groups) + 1 quan: two-sample z or t Call it a ______________ (not sure if sample is large enough to use z ) based on a matched-pairs design (see page 88). 5. 2 categorical variables: chi-square test Alternative is__________ because the training program is supposed to Response: ___________________________________________ � help. Note: 2-sample design would be better, to avoid placebo effect. Example: Terrorists’ Religion: Discrimination? Chi-Square Test (Review) Background : We want to see if Catholics were discriminated We learned to use chi-square to test for a relationship between � against, based on a table of religion and acquittals for persons two categorical variables . charged with terrorist offenses in Northern Ireland in 1991. Null hypothesis: the two variables are not related 1. Question: Which of the 5 situations applies? alternative hypothesis: the two variables are related � 2 1. 1 categorical: z test about population proportion Test stat = chi-sq = sum of (observed count-expected count) 2. 2. 1 measurement (quan) [pop sd known or sample large]: expected count z test about mean P-value= probability of chi-square this large, assuming the 3. 3. 1 measurement (quan) [pop sd unknown & sample small]: two variables are not related. For a 2-by-2 table, t test about mean chi-square > 3.84 P-value < 0.05. 4. 1 categorical (2 groups) + 1 quan: two-sample z or t If the P-value is small, conclude the variables are related. 4. Otherwise, we have no convincing evidence of a 5. 2 categorical variables: chi-square test relationship. Response: ____ � Note: Next lecture we’ll do another example of a chi-square test.
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