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What is the general linear model
Course:- Applied Statistics
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A student is interested in whether students who study with music playing devote as much attention to their studies as do students who study under quiet conditions (he believes that studying under quiet conditions leads to better attention). He randomly participates to either the music or non-music condition and has them read and study the same passage of information for the same amount of time. Subjects are given the same 10-item test on the material. Their scores appear next. Scores on the test represent interval-ratio data and are normally distributed.

Music 6, No music 10; Music 5, No music 9; Music 6, No music 7; Music 5, No music 7; Music 6, No music 6; Music 6, No music 6; Music 7, No music 8; Music 8, No music 6; Music 5, No music 9

a) What statistical test should be used to analyze these data?

b) What are H0 and Ha for this study?

c) Conduct the appropriate analysis.

d) Should H0 be rejected? What should the researcher conclude?

e) If significant, compute and interpret the effect size.

f) If significant draw a graph representing the data.

g) Determine the 95% confidence interval.

4) The researcher in exercise 2 decides to conduct the same study using a within-participants design to control for differences in cognitive ability. He selects a random sample of subjects and has them study different material of equal difficulty in both the music and no-music conditions. 

The study is completely counterbalanced to control for order effects. The data appear next. As before, they are measured on an interval-ration scale and are normally distributed; he believes that studying under quiet conditions will lead to better performance. 

Music No Music

7 7

6 8

5 7

6 7

8 9

8 8

 

a) What statistical test should be used to analyze these data?

b) What are H0 and Ha for this study?

c) Conduct the appropriate analysis.

d)  Should H0 be rejected? What should the researcher conclude?

e) If significant, compute and interpret the effect size.

f) If significant draw a graph representing the data.

g) Determine the 95% confidence interval.

 

 

  1. What are degrees of freedom? How are the calculated? 
  2. What do inferential statistics allow you to infer?
  3. What is the General Linear Model (GLM)? Why does it matter?
  4. Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other?
  5. Why is it important to pay attention to the assumptions of the statistical test? What are your options if your dependent variable scores are not normally distributed?

6) Researchers at a food company are interested in how a new spaghetti sauce made from Green tomatoes (and green in color) will compare to their traditional red spaghetti sauce. They are worried that the green color will adversely affect the tastiness scores. They randomly assign subjects to either green or red sauce condition. Participants indicate the tastiness of the sauce on a 10-point scale. Tastiness scores tend to be skewed. The scores follow:


RED SAUCE  GREEN SAUCE
7    4
5    5
9    6
10   8
6    7
7    6
8    9


a) What statistical test should be used to analyze these data?

b) Identify H0 and Ha for this study
c) Conduct the appropriate analysis
d) Should H0 be rejected? What should the researcher conclude?

8) You notice in your introductory psychology class that more women tend to sit up front, and more men sit in the back. To determine whether this difference is significant, you collect data on the seating preferences for the students in your class. Data follow:

Men Women

Front of the room  15 27
Back of the room  32 19

a) What is X2obt?

b) What is the df for this test?

c) What is X2cv?

d) What conclusion should be drawn from these results?

2. What are degrees of freedom? How are the calculated? 

3. What do inferential statistics allow you to infer?

4. What is the General Linear Model (GLM)? Why does it matter?

5. Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other?




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