Last class Tutorial 1 Census Overview URBP 204 A Class 5 Last class Tutorial 1 Census Overview THIS CLASS Normal Distribution (From Class 4) Hypothesis Testing (From Class 4) Test between means of related groups Test between means of different groups Analysis of Variance (ANOVA) Tutorial 2 Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Test between the means of related groups Source: Salkind, pg. 181 Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Test between the means of related groups Test before and after the experiment. Say, effect of watching the movie. t = 26 12x82-(26)2 12-1 = 26 28 t = 4.91 n=12 Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Steps for testing 1. Statement of null and research hypothesis H1: X1 X2 2. Set level of risk Level of risk of type I error = 5%, or level of significance (p) = 0.05 3. Selection of appropriate test statistic Choose t test for dependent means 4. Compute the test statistic (obtained t- or p-value) t= 4.91 Note: the class notes summarize Salkind (2004) Chapters 9 to 11

5. Determination of the value needed for rejection of null hypothesis (critical value) See table B2, pg. 358-359 Degrees of freedom= n-1 = 12-1 = 11 Level of risk = 0.05 1- tailed test (as directional research hypothesis) Critical value = 1.796 (with df=11; see Salkind, p.358) 6. Comparison of obtained and critical value Obtained t value is larger than the critical t value Obtained p value is smaller than the critical p value of 0.05. If you run the test is SPSS/EXCEL you will find that the obtained p value is smaller than the critical p value of 0.05. 7. Decision Reject the null hypothesis (null hypothesis- there is NO difference in the attitude towards density before and after the watching the movie) Probability is less than 5% on any one test of the null hypothesis that the average of posttest scores is greater than the average of pretest scores due to chance alone. Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Determining which test to choose Source: Salkind 2004, pg. 162 Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Test between means of different groups T-test for independent samples Examining difference between 2 groups on one variable without pretest and posttest. Simple analysis of variance If more than 2 groups Question: Whether the mean number of transit trips taken in last one month by the residents of neighborhood “1” is different than the mean number of transit trips taken by the residents of neighborhood “2” during the same time period? Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Steps for testing (see Salkind 2004, p. 164) 1. Statement of null and research hypothesis H0: Ц1 = Ц2 H1: X1 = X2 2. Set level of risk Level of risk of type I error = 5%, or level of significance (p) = 0.05 3. Selection of appropriate test statistic Choose t test for independent samples 4. Compute the test statistic (obtained value) t= -0.14 Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Steps for testing 4. Compute the test statistic (obtained value) (30-1)3.422 + (30-1)2.062 30 + 30 30 + 30 - 2 30 x 30 = 0.1 339.20 + 123.06 60 58 900 t = - 0.14 Note: the class notes summarize Salkind (2004) Chapters 9 to 11

5. Determination of the value needed for rejection of null hypothesis (critical value) See table B2, pg. 358-359 Degrees of freedom= 60-2 = 58 Level of risk = 0.05 2- tailed test (as non directional research hypothesis) Critical value = 2.001 (with df=60; see Salkind, p.359) 6. Comparison of obtained and critical value Obtained t value less smaller than the critical t value Obtained p value is larger than the critical p value of 0.05. If you run the test is SPSS/EXCEL you will find that the obtained p value is larger than the critical p value of 0.05. 7. Decision Fail to reject (accept) null hypothesis (null hypothesis - no difference in the mean number of transit trips taken by the residents of neighborhood “1” and “2”. Probability is greater than 5% that the difference between the groups may be because of chance. Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Analysis of Variance (ANOVA) Source: Salkind, pg. 195 Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Analysis of Variance (ANOVA) Test the hypothesis that parents’ education effects the size of household in a neighborhood. One treatment variable (h.h. size), but more than 2 groups (education level). Say 3 groups 1= some school (up to middle school) 2= less than high school (middle school and above) 3= high school and above Variance due to differences between individuals within groups and variance due to differences between groups are compared with each other. Note: the class notes summarize Salkind (2004) Chapters 9 to 11

Steps for testing 1. Statement of null and research hypothesis H1: X1 = X2 = X3 2. Set level of risk Level of risk of type I error = 5%, or level of significance (p) = 0.05 3. Selection of appropriate test statistic Simple ANOVA Note: the class notes summarize Salkind (2004) Chapters 9 to 11

ANOVA 4. Compute the test statistic (obtained value) F= 65.31 (note it is not t statistic this time!) 5. Determination of the value needed for rejection of null hypothesis (critical value) See table B3, pg. 362 Degrees of freedom for numerator = k-1 = 3-1 = 2 k = number of groups Degrees of freedom for denominator (number of observations) = N-k = 30-3 = 27 Level of risk (p) = 0.05 Critical value = 3.36 (see Salkind, p.362) 6. Comparison of obtained and critical value Obtained F value larger than the critical F value Obtained p value is smaller than the critical p value of 0.05. If you run the test in EXCEL/SPSS you will find that the obtained p value would be smaller than the critical p value of 0.05. Note: the class notes summarize Salkind (2004) Chapters 9 to 11

ANOVA 7. Decision Reject the null hypothesis (null hypothesis - there is NO difference between the groups). The F- value is large enough ( and the p-value is small enough) for us to say that the difference between the three groups is not due to chance. Note: the class notes summarize Salkind (2004) Chapters 9 to 11