One Factor ANOVA in Minitab As an example, we will use the data below. A study looked at the days spent in the hospital for different regions of the United States. Can the company reject the claim the mean number of days patients spend in the hospital is the same for all hour regions? Assume a = 0.05. Data can be found on the blog in anova.mtw. Data Entry Data should be in columns with level labels in each column. Multiple Box Plots Select Boxplot -> Multiple Y's (simple) and select all variable names.
Null and Alternative Hypothesis Ho: ne= mw= s= w Ha: At least one pair not equal ANOVA Table Stat -> ANOVA -> One-Way (unstacked) Conclusion There is enough evidence (F=4.98, num df = 3, den df = 29, p=0.007) to suggest that there is a difference among the regions in terms of the average number of days spent in the hospital.
Tukey Tests If the ANOVA is significant (p<.05), then return to the ANOVA (unstacked) dialog box and select Comparisons... Note, this value must equal (no decimals). Tukey Summary Northeast 7.444 Midwest 5.778 West 5.000 South 4.714
STAT 200 ANOVA Homework/Lab: One Factor Analysis of Variance Due Friday, November 20th You may work in groups, but each person is to hand in a homework assignment. Please hand in your own work, as identical homeworks will have the grade split between those working on it. For problems 1-4, state the null and alternative hypotheses. Also fill in the blanks in the ANOVA tables and state your conclusion. 1. The prices (in dollars) for 16 randomly selected automobile batteries were determined. The prices were split into three groups based on battery type. At = 0.05, can you conclude that a difference exists among battery types? Df Sum Sq Mean Sq F value Pr(>F) Size 513.42 0.1564 Error Total 2067.75 2. The following table represents the ANOVA analysis for the price per gallon for three types of exterior deck treatments. At = 0.01, can you determine if there is a difference in price based on treatment type? Df Sum Sq Mean Sq F value Pr(>F) Type 1307.92 0.001 Error 496.08 Total 14
3. From four regions across the United States, 27 school districts were sampled to determine the annual amount spent on reading in grades K-6. With = 0.05, is there a difference among spending in the four regions? Df Sum Sq Mean Sq F value Pr(>F) Region 0.215 Error 95857.14 Total 115942.23 4. The following ANOVA table shows the results for five age groups to see if there are differences in credit card balances. At = 0.05, can you determine if any age groups have different credit card balances? Df Sum Sq Mean Sq F value Pr(>F) Age 0.006 Error 23 245079.67 Total 1767327.86
5. The following is the output from a Tukey test after it was determined that the mean fuel mileage for five types of vehicles are not equal. Create a line plot/means plot to summarize the results. Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ---------+---------+---------+---------+ Small Sedan 5 43.600 5.128 (----*-----) Medium Sedan 6 54.000 7.127 (----*----) Large Sedan 6 69.500 6.656 (----*----) 4WD SUV 4 73.500 8.660 (-----*------) Minivan 5 61.400 9.711 (-----*-----) ---------+---------+---------+---------+ 48 60 72 84 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons Small Sedan subtracted from: Lower Center Upper -------+---------+---------+---------+-- Medium Sedan -3.129 10.400 23.929 (------*------) Large Sedan 12.371 25.900 39.429 (------*------) 4WD SUV 14.912 29.900 44.888 (-------*------) Minivan 3.669 17.800 31.931 (------*------) -------+---------+---------+---------+-- -20 0 20 40 Medium Sedan subtracted from: Lower Center Upper -------+---------+---------+---------+-- Large Sedan 2.601 15.500 28.399 (------*-----) 4WD SUV 5.078 19.500 33.922 (------*------) Minivan -6.129 7.400 20.929 (------*-----) -------+---------+---------+---------+-- -20 0 20 40 Large Sedan subtracted from: Lower Center Upper -------+---------+---------+---------+-- 4WD SUV -10.422 4.000 18.422 (------*------) Minivan -21.629-8.100 5.429 (------*------) -------+---------+---------+---------+-- -20 0 20 40 4WD SUV subtracted from: Lower Center Upper -------+---------+---------+---------+-- Minivan -27.088-12.100 2.888 (-------*------) -------+---------+---------+---------+-- -20 0 20 40
6. The following is the output for an ANOVA in which it has been determined that there is a difference in the mean income between the six cities listed below. Create a line plot/means plot to summarize the results. Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ---+---------+---------+---------+------ Chicago 6 44345 6037 (----*-----) Dallas 7 44017 9223 (----*----) Miami 7 42386 4571 (----*----) Denver 5 46331 4320 (-----*-----) San Diego 5 56470 6880 (-----*------) Seattle 6 66318 6724 (----*-----) ---+---------+---------+---------+------ 40000 50000 60000 70000 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons Chicago subtracted from: Dallas -11498-328 10842 (-----*----) Miami -13129-1959 9211 (-----*-----) Denver -10171 1986 14143 (-----*-----) San Diego -32 12125 24282 (-----*-----) Seattle 10382 21973 33565 (-----*-----) Dallas subtracted from: Miami -12363-1631 9100 (----*-----) Denver -9442 2314 14070 (-----*-----) San Diego 697 12453 24209 (-----*-----) Seattle 11131 22301 33471 (----*-----) Miami subtracted from: Denver -7811 3945 15701 (-----*-----) San Diego 2328 14084 25840 (-----*-----) Seattle 12763 23933 35102 (-----*-----) Denver subtracted from: San Diego -2559 10139 22837 (-----*-----) Seattle 7830 19987 32145 (-----*-----) San Diego subtracted from: Seattle -2309 9848 22006 (-----*-----)
For each of the following questions, answer them as demonstrated in lab. You will need to complete the following steps for each question: a. Create multiple box plots of the data. Make sure you include units. b. State the null and alternative hypothesis in the context of the problem. c. The ANOVA table. d. The conclusion statement in terms of the problem. Use the level of alpha given in the book. e. If the ANOVA shows significant differences, conduct a Tukey test and summarize the results using the line plot method described in class and found in the Minitab Output. f. Using the results of the analysis, answer the extra question written for each problem. Make sure your answer uses all the available information, not just the means. From Chapter 10.4 starting on page 565. 7. Question 6 Which battery size is cheaper, group size 35 or group size 65? 8. Question 10 Which type or types of cars have the lowest cost per mile, if any? 9. Question 11 Do people in the Northeast have a lower well-being index than people in the West? 10. Question 14 Which city has higher housing prices, Tampa or Orlando?