For this exercise you will use the data set Smoke Data Final 18. To understand the data, you would need to go into variable view and look at the items
8 to 27.
You would look for unusual scores which may be due to input error. Also, you need to create the new variable ID number (IDNo) or Case number (CaseNo). I have already reverse coded Q26: Cheap form of entertainment.
1. The administrator at a small undergraduate college is concerned that there seems to be an increase in the number of student smokers on the campus. She asks her assistant, Dr. Ana Lysis (Yes, she spells her name with one ‘n’ due to a misspelling on her birth certificate), to address her concern. In response, Dr. Lysis has collected data using the newly developed Smoking Cessation Index (SCI) to determine factors students deem important in smoking prevention and cessation. She has asked you to analyze the data. She has assured you that there is no missing data. Also, she has heard about some guy called Mahalonobis who identifies outliers and has asked that all such cases be deleted before conducting the analysis.
Outline the steps you take, and data issues you may have addressed before conducting any analysis.
a. She wants to know whether the SCI measures more than one underlying dimension or factor, and was advised that only items with coefficients 0.4 and above should be considered as loading on a factor. Address her concern and give the statistical evidence to support your answer.
b.
If the SCI measures more than one factor, how many factors does the SCI address and to what extent are these reliable? Please include ALL relevant tables and statistical evidence.
(Hint. Examine again Field, Ch 18. Note p. 594-600, 604-606). Also, if creating factors use the mean *5
c.
Based on your analyses thus far, with regard to smoking cessation, do the factors taken together differentiate between smokers and non-smokers? Please explain providing the relevant statistical evidence.
d.
If the groups differ, which factor or factors are significant in separating the groups? Please explain citing the statistical evidence
e.
She has asked about an equation and something about discriminant function. She wants to know if there is wine and finger-foods at the function. Please explain to her the linear discriminant function and write the equation.
f.
To avoid having to walk around the campus to see who smokes, she wants you to use the factors in an analysis to determine the percentage of students who smoke and those who do not smoke. She also wants to know the extent to which the results of the analysis are accurate.
g.
Pleased with the results, she also wants to know if the results would have been the same through random classification. Again support your answer by providing the statistical evidence.
h.
She is pleased with your work but logically asks if there are alternative analytical procedures. She asks if it is logical to analyze the data using Logistic Regression and wonders whether the results would be similar to the previous findings.
j.
She now asks if it is necessary to use all the factors in the analysis and if not,
1. Which should be excluded?
2. What would be the impact on the accuracy of the results with the removal of the factor or factors?
2.
To answer this question you will first need to run the regression analysis. Open SPSS, go to
File
– click on
New
– click on
Syntax. In the syntax window copy and paste the below syntax then click
run all. Because I have put stat=all, you will get tables not needed to answer the questions.
Make sure you include the period after teach in the last line.
Matrix data variables=rowtype_ acachv mentab ses teach.
Begin data
mean 75.533 96.967 4.233 14.533
stddev 15.163 8.915 1.455 4.392
n 30 30 30 30
corr 1.00
corr .648 1.00
corr .516 .256 1.00
corr .753 .313 .542 1.00
End data.
Regression matrix in (*)
/var=acachv,mentab,ses,teach
/descriptives=defaults corr sig
/stat=all
/dependent acachv
/method=enter mentab
/method=enter ses
/method=enter teach.
Happy with your performance, Dr. Norma L. Plot who is a colleague of Dr. Ana Lysis, asks your help in interpreting her printout. She is interested in the extent to which effective teaching accounts for variance in academic achievement. Prior research indicates that socioeconomic status (SES) and mental ability are also related to academic achievement. She hypothesizes that controlling for SES and mental ability, students with high quality teaching are more likely to have higher achievement. To test her hypothesis, she conducts a simultaneous regression analysis using SES, mental ability and teaching quality as explanatory variables.
a. Should she be concerned about multicollinearity? Give statistical evidence to support your response.
b. How much does quality teaching explain of achievement above and beyond that which is explained by mental ability and SES? Is this additional proportion significant? Give the statistical evidence to support your answer.
c. How much variance do these variables collectively account for in academic achievement and is that proportion statistically significant? Give evidence to support your answer.
d. Do you agree with her hypothesis that after controlling for SES and mental ability, students with high quality teaching are more likely to have higher achievement? Give evidence to support your answer.
e. Specific to this sample, which variable contributes most to explaining academic achievement and is this contribution significant? State your answer and supporting evidence.
f. The correlation between SES and academic achievement is .516 and the regression coefficient
b =
1.021. However, SES is not a significant predictor of academic achievement. How is this possible? Again give supporting evidence for your response.
g. From the study Dr. Plot concludes that while SES may not be a significant predictor of academic achievement, students with higher SES get better quality teaching which results in higher academic achievement. Do you agree with her conclusion? Give evidence to support your response.