Unit 9 lesson 1
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This document discusses planned contrast ANOVA, which allows researchers to test specific hypotheses about group mean differences rather than an overall hypothesis. It provides an example comparing IQ scores of blondes, brunettes and redheads. Researchers can create contrast variables to test the hypotheses that blonde and brunette means equal each other and that blonde and brunette means together equal the redhead mean. Planned contrast ANOVA merges regression and ANOVA techniques to test these focused hypotheses rather than an overall difference in means.
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1. Consider the following partially completed computer printout fo.docx
1. Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive.
Based on the information provided, what is the F statistic?
About 8 .33
Just over 2.35
About 4.76
About 69.5
4 points
QUESTION 2
1. The standard error of the estimate is a measure of
total variation of the Y variable.
the variation around the sample regression line.
explained variation.
the variation of the X variable.
4 points
QUESTION 3
3.Nintendo Sony would like to test the hypothesis that a difference exists in the average age of users of a Wii, a PlayStation, or an Xbox console game. The following data represent the age of a random sample of Wii, PlayStation, and Xbox users.
Wii
PlayStation
Xbox
37
26
31
31
21
20
47
24
38
29
24
31
36
25
30
Using α = 0.05, the conclusion for this hypothesis test would be that because the test statistic is
more than the critical value, we cannot conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game.
less than the critical value, we cannot conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game.
more than the critical value, we can conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game.
less than the critical value, we can conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game.
4 points
QUESTION 4
1. The relationship of Y to four other variables was established as Y = 12 + 3X1 - 5X2 + 7X3 + 2X4. When X1 increases 5 units and X2 In a sample of n = 23, the Student's t test statistic for a correlation of r = .500 would be:
2.559
2.819
2.646
can’t say without knowing α (alpha)
4 points
QUESTION 5
1. Given the following ANOVA table (some information is missing), find the F statistic.
3.71
0.99
0.497
4.02
4 points
QUESTION 6
1. Examine the following two-factor analysis of variance table:
Complete the analysis of variance table.
MSA = 40.928, F Factor A =3.35, SSB = 85.35, Factor B df = 3, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 1.8, SSE = 789.29, SSE df = 66, MSE = 12.143
MSA = 40.928, F Factor A = 3.35, SSB = 85.35, Factor B df = 4, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 2.1 SSE = 789.29, SSE df = 66, MSE = 12.143
MSA = 40.698, F Factor A = 3.35, SSB = 84.35, Factor B df = 5, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 2.1, SSE = 789.29, SSE df = 65, MSE = 12.143
MSA = 40.698, F Factor A = 3.35, SSB = 84.35, Factor B df = 3, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 1.8, SSE = 789.29, SSE df = 65, MSE = 12.143
4 points
QUESTION 7
1. The critical value for a two-tailed test of H0: ß1 = 0 at a (alpha) = .05 in a simple regression with 22 observations is:
+ or - 1.725 ...
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JKN 10 Inference 2 Populations.Consider the following set of d.docx
JKN 10 Inference 2 Populations.
Consider the following set of data.
Pairs
1
2
3
4
5
Sample A
9
4
3
5
3
Sample B
3
8
2
7
1
(a) Find the paired differences, d = A - B, for this set of data.
(d1)
(d2)
(d3)
(d4)
(d5)
(b) Find the mean d of the paired differences. (Give your answer correct to one decimal place.)
(c) Find the standard deviation sd of the paired differences. (Give your answer correct to two decimal places.)
Salt-free diets are often prescribed to people with high blood pressure. The following data values were obtained from an experiment designed to estimate the reduction in diastolic blood pressure as a result of consuming a salt-free diet for 2 weeks. Eight subjects had their blood pressure measured and then ate a salt free diet for two weeks and had their blood pressure measured again. Assume diastolic readings to be normally distributed.
Before
99
105
93
102
100
108
107
97
After
92
102
91
94
96
98
100
93
(a) The proper TI-83 program to use to compute the confidence interval for the mean reduction in blood pressure is:
(b) Find the 98% confidence interval for the mean reduction. (Give your answers correct to two decimal places.)
Lower Limit
Upper Limit
(c) Which of the following statements is true about the confidence interval? (More than one may apply)
We are 98% confident that the true mean of the individual differences in blood pressure is in the intervalIf we took 100 samples and constructed 100 confidence intervals for the mean of the individual differences, approximately 98 of them would contain the true mean of the individual differencesWe are 98 % confident that the mean of the after data minus the mean of the before data is in the intervalWe are 98 % confident that the mean of the before data minus the mean of the after data is in the interval
An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were litter-mates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown in the following table. Assuming weight gain is normal, find the 99% confidence interval estimate for the mean of the differences μd, where d = ration A - ration B. (Give your answers correct to two decimal places.)
Litter
1
2
3
4
5
6
7
8
Ration A
56
40
60
59
43
40
50
46
Ration B
54
30
50
56
37
36
42
40
Lower Limit
Upper Limit
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims.
(a) There is an increase in the mean difference between post-test and pretest scores.(d=post-test scores - pretest scores)
Ho: μd
0
Ha: μd
0
(b) Following a special training session, it is believed that the mean of the difference in performance scores will not be zero.
Ho: μd
0
Ha: μd
0
(c) On average, there is no difference between the readings from two inspectors on .
Project for MA135 You are doing research on balance and fitn.docx
Project for MA135
You are doing research on balance and fitness. To complete this research you will need a watch with a second hand. Identify a random sample of n = 12 men and n = 8 women. You must answer this question: How do you establish that this sample is truly random?
Have each subject perform the following task:
1. Have the subjects stand with their hands at their side, raise one knee, cross their ankle over the other knee, squat and bring their hands palms together in front of their chest. Time the subject until they put their foot back down on the floor.
b) Ask the following questions:
i) How many days per week do they exercise?
ii) What is their favorite exercise?
You will analyze your data and compute the following statistics for each group:
1) The Mean and standard deviation of the number of seconds the subject stayed balanced
2) The Median number of days per week exercised
3) The Mode of the favorite exercise
4) The 90% confidence interval of the mean
5) Construct a complete hypothesis test and determine if the two groups have significantly different balance using α = 0.05.
Write a
one page introduction to your research, discuss how you selected your sample (is it a random sample?), and
write a one page conclusion. Present your data in an organized manner.
Research Project Rubric
Organization: Maximum of 10 points
Overall report is well organized, with a cover page, introductory page, discussion of sampling, all data is shown, statistics are clearly presented, and conclusion page.
(Points are deducted for presentation, missing information).
Statistics: Maximum of 40 points
Mean for each group is correct (8 points)
Standard deviation for each group is correct (8 points)
Median for each group is correct (8 points)
Mode for each group is correct (8 points)
Confidence interval of the mean for each is correct (8 points)
Hypothesis Test: Maximum of 30 points
Null and Alternate Hypothesis are stated correctly (6 points)
Critical t value is correct (6 points)
Computation of the t statistic is correct (6 points)
Decision regarding the hypothesis is correct (6 points)
Conclusion regarding the hypothesis is correct (6 points)
Writing: Maximum of 20 Points
Overall writing is thorough with correct grammar, punctuation,
spelling, and capitalization.
(Points are deducted for quality and mechanics).
Extra Credit: Maximum of 5 points
Graphics, graphs… Wow me!
2
After downloading the excel data generator, please take a screen shot like below then attach it on the first page of the project.
Figure 1Excel data generator
Figure 2
If you do not attach, you will lose 10% of the grade.
After downloading the excel data generator, please take a screen shot like below then attach it on the first page of the project.
Sample Cover page
MA-135(Section #):
Title
Figure 3Picture
.
Nonparametric and Distribution- Free Statistics _contd
This document summarizes the Wilcoxon signed-rank test, a nonparametric test used to test hypotheses about the median or location of a population when the assumptions of the t-test are not met. It provides an example applying the test to data on cardiac output measurements from 15 patients. The test calculates the differences between each observation and the hypothesized median, ranks the absolute values of the differences, and sums the ranks with positive and negative signs. The smaller of the two sums is the test statistic, which is compared to a critical value to determine if the null hypothesis that the population median equals the hypothesized value can be rejected.
Question 1 (25 points)Question 1 optionsEnter the answer to.docx
Question 1 (25 points)
Question 1 options:
Enter the answer to each of the of the questions with:
T for True
F for False
a. If the variance from a data set is zero, then all the observations in this data set must be identical.
b. P(A and Ac) = 1 where Ac is the compliment of A.
c. The mean is always equal to the median for a normal distribution.
d. A 99% confidence interval is wider than a 95% confidence interval of the same parameter.
e. It is easier to reject the null hypothesis if we use a smaller significance level (alpha).
Question 2 (4 points)
A random sample of 25 customers was chosen in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).
Checkout Time (in minutes)
Frequency
Relative Frequency
1.0 - 1.9
4
A
2.0 - 2.9
B
.4
3.0 - 3.9
C
D
4.0 - 5.9
5
E
Total
25
F
Complete the Frequency Table with the missing frequency and relative frequency numbers.
Enter answer for "A" with 2 decimal place acueacy.
Enter answer for "B" as an integer.
Enter answer for "C" as an integer.
Enter answer for "D" as an integer.
Enter answer for "E" with 2 decimal place acueacy.
Enter answer for "F" as an integer.
Question 3 (5 points)
Question 3 options:
A random sample of 25 customers was chosen in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).
This is the same table from the previous question.
Checkout Time (in minutes)
Frequency
Relative Frequency
1.0 - 1.9
4
2.0 - 2.9
0.4
3.0 - 3.9
4.0 - 5.9
5
Total
25
What percentage of the checkout times was at least 3 minutes?
Enter answer as a percent without the percent sign to 0 decimal places.
Question 4 (5 points)
Question 4 options:
A random sample of 25 customers was chosen in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).
This is the same table from the previous question with the Interval column added.
Interval
Checkout Time (in minutes)
Frequency
Relative Frequency
1
1.0 - 1.9
4
2
2.0 - 2.9
0.4
3
3.0 - 3.9
4
4.0 - 5.9
5
5
Total
25
In what class interval must the median lie?
Enter answer with the appropriate Interval number.
Question 5 (5 points)
Question 5 options:
A random sample of 25 customers was chosen in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).
This is the same table from the previous question.
Checkout Time (in minutes)
Frequency
Relative Frequency
1.0 - 1.9
4
2.0 - 2.9
0.4
3.0 - 3.9
4.0 - 5.9
5
Total
25
Assume that the largest observation in this dataset is 4.8. Suppose this observation were incorrectly recorded as 8.4 instead of 4.8.
Will the ...
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JKN 10 Inference 2 Populations.Consider the following set of d.docx
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Project for MA135 You are doing research on balance and fitn.docx
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Nonparametric and Distribution- Free Statistics _contd
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Question 1 (25 points)Question 1 optionsEnter the answer to.docx
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Unit 9 lesson 1
- 1. Unit 9: Planned Contrast ANOVA Lesson 1: Merging Regression and ANOVA EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Planned Contrast Next Slide
- 4. Creating Contrast Variables Contrasts reflect the associations that we want to test Contrast 1 tests H 0 : M blondes =M brunettes Contrast 2 tests H 0 : M blondes & brunettes =M redheads Next Slide Maximum number of contrasts = K –1 -2 0 111.5 Redheads 1 -1 107 Brunettes 1 1 105 Blondes Contrast 2 Contrast 1 Mean
- 5. Practice Contrast Variables C1 – H 0 : M white =M black C2 – H 0 : M asian and hisp. =M nat.amer. C4 – H 0 : M w,a,na. =M b C3 – H 0 : M w,b,h,na =M a Next Slide 1 1 -2 0 Native American 0 1 1 0 Hispanic 1 -4 1 0 Asian -3 1 0 -1 Black 1 1 0 1 White C4 C3 C2 C1
- 6. Back to “IQ” – “Hair” Example Next Slide
- 7. Regression as ANOVA Analyze Regression Linear Next Slide
- 8. Planned Contrast ANOVA Output Next Slide
- 9. Planned Contrast ANOVA Output (cont.) SS c2 = 88.667 – 8.0 = 80.667 F-crit on 1 and 9 df = 5.12 Next Slide SS c2 =SS 2 regression – SS 1 regression Y N
- 10. Smart vs. Not-Smart Researchers Next Slide
- 11. A New Example Next Slide You will have 5 “Blocks.” C1 in Block 1; C2 in Block 2; etc.
- 12. SPSS Output for “New Example” Next Slide SS c2 =.333 - .250 SS c3 =.375 - .333 SS c4 =.400 - .375 SS c5 =370.417 - .400
- 13. Results for “New Example” Next Slide F-crit on 1 and 6 df = 5.99
- 14. “Other” Examples Next Slide -1 -1 -1 0 Group 5 -1 -1 1 0 Group 4 4 0 0 0 Group 3 -1 1 0 -1 Group 2 -1 1 0 1 Group 1 C4 C3 C2 C1
- 15. Unit 9: Planned Contrast ANOVA Lesson 1: Merging Regression and ANOVA EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Planned Contrast