Statistics I – Second Analysis Project

You are part of a research team that is interested in comparing the effectiveness of two different methods for teaching physical science to middle school students. In particular, they wish to compare two individualized computer based instruction programs. One is based on behavioristic principles while the other is based on principles of cognitive theories. A sample of students is randomly selected. Individuals in the sample are then randomly assigned to one of the two instructional programs. After completing the computer-based instruction each student is given the new state physical science test. Although there are many outcomes of potential interest, this study focuses on achievement as measured by the state physical science achievement test.

The research team wishes to estimate the size of the effect and to conduct a statistical test with a set to .05. For this project you should analyze the data and write a short summary of the results. Please turn in (1) the summary, (2) the program, and (3) the output.

A group of biochemistry researchers developed a new medication for treating depression. To assess if the new medication is effective at treating depression, the researchers obtained a sample of depressive patients from a local clinic. The patients were then randomly assigned into taking the medication for a month or not. In addition, the patients were also randomly assigned into receiving psychotherapy for a month or not. At the end of the study, the patients were asked to fill out a depression inventory in which a higher score indicates more depression. The data are below. What can be concluded with α = 0.05?

                Psychotherapy

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Medication: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Psychotherapy: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Interaction: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Medication: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Psychotherapy: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is a medication difference in depression.There is no medication difference in depression.    

There is a psychotherapy difference in depression.There is no psychotherapy difference in depression.    

There is a medication by psychotherapy interaction in depression.There is no medication by psychotherapy interaction in depression.    

A social psychologist is interested in how optimism is related to life satisfaction. A sample of individuals categorized as optimistic were asked about past, present, and projected future satisfaction with their lives. Higher scores on the life satisfaction measure indicate more satisfaction. Below are the data. What can the psychologist conclude with α = 0.01?

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² =  ;  ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

At least one of the temporal means is different on life satisfaction.None of the temporal means is different on life satisfaction.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =  ; significant:  ---Select--- Yes No
2 vs. 3: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No
1 vs. 3: test statistic =  ; significant:  ---Select--- Yes No

How does gender and occupational prestige affect credibility? Graduate students in a public health program are asked to rate the strength of a paper about the health risks of childhood obesity. In reality, all student raters are given the same paper, but the name and degree associated with the author are changed. The student raters are randomly assigned to one group from the following name ("John Lake", "Joan Lake") and degree (M.D., R.N., Ph.D.) combination. The raters score the paper from 1 to 5 on clarity, strength of argument, and thoroughness. The total scores (the sum of the three scores) are given in the table below. What can be concluded with an α of 0.01?

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Name: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Degree: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Interaction: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Name: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Degree: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is a name difference in the total scores.There is no name difference in the total scores.    

There is a degree difference in the total scores.There is no degree difference in the total scores.    

There is a name by degree interaction in the total scores.There is no name by degree interaction in the total scores.    

A researcher is studying the effects of inserting questions into instructional material for learning. There is doubt whether these questions would be more effective before or after the corresponding passage. In addition, the researcher wants to know the impact of factual and thought provoking questions. Students are randomly assigned to one of each of the four combination: position of question (before vs. after the passage) and type of question (factual vs. thought provoking). After 20 hours of studying under these conditions, the students are given a test on the content of the instructional materials. The test scores are below. What can be concluded with α = 0.05? Please use 4 numbers after decimal

                     Position

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Type: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Position: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Type: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Position: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is a question type difference in the test scores.There is no question type difference in the test scores.    

There is a question position difference in the test scores.There is no question position difference in the test scores.    

There is a question type by position interaction in the test scores.There is no question type by position interaction in the test scores.    

Question 1

What percent of the variance in salary is explained by knowing years of experience and average evaluations?

How do I calculate the y intercept, slope, and MSE?

What is the formula using RStudio to plot these 3 columns of data?

Assume that a procedure yields a binomial distribution with 4 trials and a probability of success of 0.60 Use a binomial probability table to find the probability that the number of successes is exactly 4.

The probability that the number of successes is exactly 4 is nothing.

A shop sells helium balloons in eight different colours: red, pink, yellow, blue, green, purple, black and silver. (a) How many different selections of 16 helium balloons can be purchased if the shop has at least 16 balloons of each colour in stock? (b) How many different selections of 16 helium balloons can be purchased if you buy at least 3 red balloons and at least 5 yellow balloons, and the shop has at least 16 balloons of each colour in stock? (c) How many different selections of 16 helium balloons can be purchased if the shop has only 7 pink balloons in stock and only 5 blue balloons in stock, but at least 16 balloons of each other colour in stock?

What will the generic confounding pattern be for a 2^5-2 (resolution III) experiment design?

Suppose that in an automatic filling process of oil in cans, the content of cans the content of cans in gallons is Y= 50 + X where x is a random variable with density f(x)=1-|x| when |x| ≤0 and 0 when|x| >0, in a lot of 100 cans how many will contain 50 gallons or more? What is the probability that a can will contain less than 49.5 gallons less than 49 gallons? Also find F(x).

A game is to be played by first flipping a fair coin, and then drawing balls without replacement from a bin. If you flip heads you get to draw one ball, and if you flip tails you get two draw two balls. The bin contains 7 red balls, and 4 white balls. Let W = 4^x - 2 be your win amount, where X represents the number of white balls drawn. What is your expected win amount on any given play?

A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean 60 thousand miles and a standard deviation of 11 thousand miles.

How many miles will be traveled by at least 65% of the truck?
The number of miles that will be traveled by at least 65% of the truck is ____ miles