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STAT141 Lecture Notes - Lecture 93: Null Hypothesis, Coefficient Of Determination, Analysis Of Variance

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whitehorse397
14 Oct 2016
School
University of Alberta
Department
Statistics
Course
STAT141
Professor
James Muriithi

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Answers
Use SPSS to answer the research question. Post your response to the following:
1.What is your research question?
The research question is whether the “RS HIGHEST DEGREE” has any impact on the
family income or not i.e. is there a significant difference between the average family
income for different highest degrees?
2.What is the null hypothesis for your question?
The null hypothesis is that the average family income is same for any highest degree,.
And the alternative is that at least one group has different mean family income.
3.What research design would align with this question?
I am comparing the mean among more than 2 groups thus a one way ANOVA is the
most appropriate test in this case.
4.What dependent variable was used and how is it measured?
The dependent variable is FAMILY INCOME IN CONSTANT $ (realinc) and it is
measured in quantitative (ratio) scale with $ as the unit of measurement.
5.What independent variable is used and how is it measured?
The independent variable is RS HIGHEST DEGREE (degree) and it is measured in
qualitative (ordinal) scale.
6.If you found significance, what is the strength of the effect?
The obtained output is given below,
Model Summary
Model
R
R Square
Adjusted R
Square
Std. Error of the
Estimate
1
.419a
.176
.175
32274.505
a. Predictors: (Constant), RS HIGHEST DEGREE
Coefficientsa
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Document Summary

The null hypothesis is that the average family income is same for any highest degree,. And the alternative is that at least one group has different mean family income. I am comparing the mean among more than 2 groups thus a one way anova is the most appropriate test in this case. The dependent variable is family income in constant $ (realinc) and it is measured in quantitative (ratio) scale with $ as the unit of measurement. The independent variable is rs highest degree (degree) and it is measured in qualitative (ordinal) scale. 22. 187: dependent variable: family income in constant $ The value of r-square shows that there is a relationship between the two values. 17. 6% of the changes in the income are explained by the changes in highest degree. 7. explain your results for a lay audience and further explain what the answer is to your research question.

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

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Related Questions


2. (12 marks) In a study of 85 individuals, food questionnaires were used to measure the change in polyunsaturated fatty acids (PUFA) intake from the beginning to the end of the study. In addition researchers measured a genetic marker in the TNF-αgene; for this analysis, we will take the two values of this TNF-αvariable to be A- or A+. The researchers also collected information on gender, age and BMI. The primary question of interest is whether TNF-αmodifies the effect of PUFA on HDL.
 
(a) (1 mark) Let TNFa be a variable with value 1 for A+ and 0 for A- TNF-αstatus and
let gender be 1 for males and 0 for females. State a linear model for mean change in HDL that includes the predictors PUFA, TNFa, PUFA×TNFa interaction, and effects for gender, age and BMI.
(b) (1 mark) A summary of the fitted model is:
                     Estimate       Std. Error   t value     Pr(>|t|)
(Intercept)     0.037531      0.196980   0.191     0.8494
pufa              0.019143      0.009245    2.071      0.0417
TNFa              0.074433      0.034128   2.181      0.0322
gender          -0.008988      0.031793   -0.283     0.7781
age               -0.003895      0.002156   -1.806     0.0747
bmi                0.006777      0.004332    1.565      0.1217
pufa:TNFa      -0.024575      0.017844  -1.377      0.1724
Write a short sentence to describe why we would even consider removing gender from the model (i.e., why we would not just be happy with the above model from
the outset).
 
(c) (2 marks) Below is a summary of the model fit without gender. Using our 10% rule-of-thumb, is there any evidence that gender confounds the PUFA×TNFa effect?
If so why, if not why not?
                        Estimate     Std. Error      t value       Pr(>|t|)
(Intercept)       0.024467     0.190364      0.129         0.8981
pufa                0.018841     0.009130      2.064         0.0423
TNFa               0.074850     0.033897      2.208         0.0301
age                -0.003783     0.002107    -1.795         0.0765
bmi                 0.006835     0.004301     1.589          0.1161
pufa:TNFa       -0.024496     0.017737   -1.381          0.1712
 
(d) (2 marks) The researchers decided to use the model with PUFA, TNFa, PUFA×TNFa, age and BMI for inference of PUFA×TNFa interaction. What are the degrees of
freedom for the t-distribution whose critical value we need to construct confidence intervals for the interaction? What upper tail probability should you use for a 95%
confidence interval?
(e) (1 mark) The appropriate critical value is 1.96. Construct a 95% confidence interval for the interaction.
(f) (2 marks) State the null hypothesis and a two-sided alternative hypothesis for testing whether TNFa modifies the effect of PUFA on HDL.
(g) (1 mark) From the computer output, what is the p-value for this test?
(h) (2 marks) For fixed age and BMI, what is the estimated effect of a one-unit change in PUFA for a subject who is A- at TNF-α? For fixed age and BMI, what is the estimated effect of a one-unit change in PUFA for a subject who is A+ at TNF-α.