Assume that a researcher interested in growth spurts among young teens decided to measure the height difference between boys and girls in middle school from a random sample of 200 boys and girls. In this study, what are the two variables of interest and which of the two variables is the independent variable and the other, the dependent variables?

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Independent Samples t-Tests

Chapter Objectives
The reader will be able to:
-Understand the use of Independent Samples t Test as a test of two independent sample means
-Understand the role of independent and dependent variables
-Understand the concept of standard error of the difference between means as the average expected difference between two random samples from two different populations on a measurement
-Interpret the results through the probability level that the null -hypothesis is true

Exercise for Chapter 22
Factual Questions

1. What is the scenario when performing an Independent Samples t Test is required?

2. Assume that a researcher interested in growth spurts among young teens decided to measure the height difference between boys and girls in middle school from a random sample of 200 boys and girls. In this study, what are the two variables of interest and which of the two variables is the independent variable and the other, the dependent variables?

3. In the above scenario, state the null and the alternative hypotheses.

4. If alternative hypothesis is as follows: H A: 1 2, and you rejected the null hypothesis in favor of the alternative hypothesis, state in words what you would conclude.

5. The above alternative hypothesis would be (circle one)?
A. Nondirectional hypothesis
B. Directional hypothesis

6. In another study, if the alternative hypothesis is
1 <
2 , and you concluded in favor of the alternative hypothesis, in words what you would conclude?

7. The above alternative hypothesis would be (circle one)?
A. Nondirectional hypothesis
B. Directional hypothesis

8. Generally, the larger the samples, the smaller the standard errors become, increasing the likelihood of finding statistical significance. This statement is (circle one)?
A. True
B. False

9. Calculating the standard error of the difference between means depends on the standard deviations as well as the sample sizes between the groups, and can be considered equal or unequal. This statement is (circle one)?

A. True
B. False
10. What do the following results indicate in terms of rejecting the null hypothesis: (t = 3.20, df = 28, p < .05, two-tailed test)?

Question for Discussion
11. Give an example of one continuous data and one categorical data with two categories that would require performing an Independent Samples t Test.

Notes
1. If the sample sizes or the standard deviations are very different between the two independent groups, one needs to consider nonparametric tests such as the Mann–Whitney U test as an alternative.
2. A full explanation about the degrees of freedom is beyond the scope of this book.
3. Review Chapter 20 on probability.

Example 1 mentions how many possible explanations for the 3-point difference? What is the name of the hypothesis which states that the observed difference is due to sampling errors created by random sampling? If there is no variation among members of a population, is it possible to have sampling errors when sampling from the population?

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Introduction to the t-Tests

Chapter Objectives
The reader will be able to:
Understand the concept of t test as a test of the difference between two sample means to determine statistical difference n Understand the factors affecting the probability level that the null
hypothesis is true n Understand the difference among independent samples, paired samples, and one sample t tests Researchers frequently need to determine the statistical significance of the difference between two sample means. Consider Example 1, which illustrates the need for making such a comparison. This chapter deals with how to compare two sample means for statistical significance. About a hundred years ago, a statistician named William Gosset developed the t test for exactly the situation described in Example 1 (i.e., to test the difference between two sample means to determine whether there is a significant difference between them or statistical significance).1 As a test of the null hypothesis, the t test yields a probabil- ity that a given null hypothesis is correct. As indicated in Chapter 20, when there is a low probability that it is correct—say, as low as .05 (5%) or less—researchers usually reject the null hypothesis. The computational procedures for conducting t tests are beyond the scope of this book. 2 However, the following material describes what makes the t test work. In other words, what leads the t test to yield a low probability that the null hypothesis is correct for a given pair of means? Here are the three basic factors, which interact with each other in determining the probability level:

Exercise for Chapter 21
Factual Questions
1. Example 1 mentions how many possible explanations for the 3-point difference?

2. What is the name of the hypothesis which states that the observed difference is due to sampling errors created by random sampling?

3. Which of the following statements is true (circle one)?
A. The t test is used to test the difference between two sample means to determine statistical significance.
B. The t test is used to test the difference between two population means to determine statistical significance.

4. If a t test yields a low probability, such as p < .05, what decision is usually made about the null hypothesis?

5. The larger the sample, the (circle one)
A. more likely the null hypothesis will be rejected.
B. less likely the null hypothesis will be rejected.

6. The smaller the observed difference between two means, the (circle one)
A. more likely the null hypothesis will be rejected.
B. less likely the null hypothesis will be rejected.

7. If there is no variation among members of a population, is it possible to have sampling errors when sampling from the population?

8. If participants are first paired before being randomly assigned to experimental and control groups, are the resulting data “independent” or “dependent”?

9. Which type of data tends to have less sampling error (circle one)?
A. Independent
B. Dependent

Notes
1. As indicated in Chapter 20, when a result is statistically significant, the null hypothesis is rejected.
2. See Appendix A for the computational procedures for t tests for reference.
3. In the types of studies we are considering, researchers do not know the variation in population.

However, the t test uses the standard deviations of the samples to estimate the variation of the population. In other words, the standard deviations of the samples provide the t test with an indication of the amount of variation in the populations from which the samples were drawn. Pyrczak, Fred, and Deborah M. Oh.

4. Ideally, we would like to conduct an experiment in which the two groups are initially identical in their visual acuity.

5. The formulas for the standard error of the difference between means are different for Independent Samples t Test and Dependent t Test. These along with the formula for the Standard error of mean are listed in Appendix A. = 0

Why do you consider them the most innovative works? What about them is innovative? How did they influence later artists? Who were the later artists that they influenced?

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Final

In a 3 page essay, discuss, from your readings, what you consider the three most innovative artworks or buildings from the Prehistoric Period through the Late Gothic / Proto-Renaissance Period (30,000 BCE to the 1300s CE) (chapters 1 through 14 of Gardner’s Art Through the Ages). Your three choices must come from the course textbook and the works we studied in class. You can choose any work from your Homework lists.

Answer the following questions in a well crafted essay (that includes an Introduction, Body and Conclusion).

1) Why do you consider them the most innovative works? What about them is innovative?

2) How did they influence later artists? Who were the later artists that they influenced?

Describe and explain each of your choices fully (including their formal elements). Include specific artists, titles, dates and styles, and use terms from your textbook to illustrate your points.

Compare and contrast the English system and the metric system of linear measure. What is the origin of each? Are there advantages or disadvantages to either system? If you had a choice, which system would you teach your class as a primary system of measurement?

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Answer peer discussion questions

Instructions on responding to peer discussion questions:

The following are examples of online participation (according to the Classroom Policies – Student Expectations document from the Student Success Center):

  • Follow-up responses to classmate’s initial DQs that integrate course theories with a practical application of the subject, perhaps offering a personal observation or experience, or referencing real-world examples, current events, or presenting further research you have conducted on the topic
  • Interaction in classroom discussion that demonstrates deeper or broader thoughts about a topic, rather than just rephrasing what the textbook has presented on the topic
  • Posts that encourage further discussion and ongoing dialogue with other students and the instructor in the class
  • Asking additional, relevant questions about the week’s topic
  • Communications that are presented in a professional and supportive manner, and with respectful tone

 

Respond to the following discussion questions individually.

Discussion topic is Compare and contrast the English system and the metric system of linear measure. What is the origin of each? Are there advantages or disadvantages to either system? If you had a choice, which system would you teach your class as a primary system of measurement?

Write an essay paper on how the push towards college is overpowering the possibilities within the trades, persuasive towards trades and how they can be a benefit to kids who don’t think college is right for them, showing how tradesman can make just as much without a college degree.

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College vs. Trade School

Write an essay paper on how the push towards college is overpowering the possibilities within the trades, persuasive towards trades and how they can be a benefit to kids who don’t think college is right for them, showing how tradesman can make just as much without a college degree.

When it comes to using SPSS, what do you find as most helpful and most difficult? Explain what descriptive statistics are and a few keys to understand for using them in student success initiatives. Explain how inferential statistics work and why they can help us in advancing student success.

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SPSS Reflection

1) When it comes to using SPSS, what do you find as most helpful and most difficult?

2) For 2A and 2B assume that you are writing a short paragraph summary to a candidate entering Stats at the start of next semester…

A: Explain what descriptive statistics are and a few keys to understand for using them in student success initiatives.

B: Explain how inferential statistics work and why they can help us in advancing student success.

3) Discuss how theory should influence our work as a researcher.

4) What are your top three take-aways from Dan Willingham’s When can you trust the experts? Why?

5) Complete this final task by reflecting on your development and next steps: what topic(s) and/or idea(s) have had the most impact on you this semester? And what questions do you want to dive into next, thinking about quantitative research?

Requirements

Submit a Word document that includes clearly organized responses to each of the prompts listed on this reflection. Your total narrative should be no more than 3-4 full pages and ought to integrate citations, where appropriate.

Create a graph that you think is helpful in presenting some relevant descriptive statistics and a short one paragraph (max) narrative explaining the visual and what it represents regarding your data set.

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Basics of SPSS Assignment

 Overview

In this short task you are going to log into SPSS, create specific variables, code the variables correctly given the types of each variable, input data, and run descriptive statistics to demonstrate your ability to do these basic essentials of data entry, refinement, and analysis.  You will submit your output and the data file to Dropbox.

Step-by-Step Tasks

  • Log into the virtual server
  • Start up the SPSS program
  • Create a new/blank data sheet
  • Create the variables listed below and code them appropriately for the following columns in Variable View: (a) Name, (b) Type, (c) Label, (d) Values, and (e) Measure – you can do the others if you would like but they are not required
  • Input the data on the second page
  • Run descriptive statistics overall
  • Run descriptive statistics after splitting the data file by chosen major (Major)
  • Create a graph that you think is helpful in presenting some relevant descriptive statistics and a short one paragraph (max) narrative explaining the visual and what it represents regarding your data set.

 

Variables to Include

You will create variables for each of the following types of information:

 

Name – the participant’s name

Gender – the participant’s biological sex

Race – the participant’s race

(Options: American Indian, Asian, Black, Hispanic, White, Other)

High School GPA – the participant’s GPA from their high school transcript

AP Credits – the number of AP credits earned by the participant during high school

Freshman Year GPA – the grade point average of the student during their first full year on campus

Major – the participant’s selected major

(Options: History, English, Computer Science, Biology, Education, Other)

Logic Training – the participant’s experience in taking courses/training in logic offered by the university as part of their first year encouraged opportunities

(Options: Lots, Some, None)

 

** Hint: in SPSS your “Name” category cannot use spaces so you have to code each variable and are encouraged to use the “label” category to specific exactly what the variable is **

 

Submission Requirements

  • Create a Word document that includes copied output data for tasks #6, 7, and 8 in an organized fashion
  • Save your dataset and submit it (this will be a type “SPSS Statistics” .sav file)

 

Name Gender Ethnicity HS GPA AP Credits Freshman GPA Major Logic Training
Akbar M Black 2.78 0 3.20 Comp Sci None
Benito M Hispanic 2.99 0 2.80 Education None
Chan M Asian 4.00 9 4.00 History Lots
Danisha F Black 3.62 3 3.60 Other Lots
Everly F White 3.65 9 3.20 Education None
Fred M White 3.22 0 2.00 English None
Gabriel M Hispanic 3.31 0 3.45 Biology Some
Heather F White 3.40 0 2.25 Education None
Ian M White 3.12 0 3.25 History Some
Juanita F Hispanic 2.67 0 3.40 English Lots
Kyeong F Asian 3.87 9 3.40 Education None
Larry M White 3.15 0 1.60 Comp Sci None
Meredith F White 3.65 6 4.00 Education Some
Naomi F Black 3.20 3 1.75 English None
Olivia F White 3.33 0 3.30 History Some
Paddington M White 3.10 0 3.20 Comp Sci Some
Quinton M Black 2.95 0 3.55 Comp Sci Lots
Rachel F White 3.55 0 4.00 Biology Some
Sampson M White 2.90 0 3.10 History Some
Tomas M Hispanic 2.75 0 3.60 Comp Sci Lots
Uther M White 3.70 6 3.60 Biology None
Victoria F Asian 3.65 6 3.55 Other Some
Wilma F White 3.08 0 3.15 Biology Some
Xerxes M Amer Ind 2.75 0 3.80 Comp Sci Lots
Yolanda F Hispanic 3.72 6 3.00 Education None
Zachariah M White 3.68 3 3.60 Other Some

 

Is there a relationship between student score on the local mathematics exam and their performance on the state mathematics exam?

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Correlation Assignment

Steps

  • Download the “RelationshipDataForClass” .SAV file from D2L
  • Open up SPSS and open the .SAV file you just downloaded
  • Either from memory or using the PPT slides + Field textbook, complete the steps of hypothesis testing for the data file
    1. Research Question: Is there a relationship between student score on the local mathematics exam and their performance on the state mathematics exam?
  • Your assignment submission is a Word document that includes the following:
    1. Just the output table that shows the “Correlations” results
    2. Answer the following questions briefly (1-2 sentences max each)
      1. Does this analysis violate the assumption of linearity? How do you know?
      2. What is the actual r-statistic you will report for this analysis with regards to the following specific relationships (loctest & stexam)?
  • What is the p-value with regards to each of the r-statistics reported in 4-b-ii?
  1. Write up a one-paragraph simple interpretation that summarizes the findings
  • Submit the Word document including your answers to (a) and (b: i-v) to Dropbox by the deadline

 

 

 

Does the format of delivery impact student performance on an end of course multiple choice exam? Does this analysis violate the assumption of homogeneity of variance? How do you know? What is the actual t-statistic you will report for this analysis with regards to student performance on the multiple choice exam? What is the p-value with regards to student performance on the multiple choice exam?

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T-Test Assignment

Steps
1) Download the “LectureVFlippedDataForClass” .SAV file from D2L

2) Open up SPSS and open the .SAV file you just downloaded

3) Either from memory or using the PPT slides + Field textbook, complete the steps of hypothesis testing for the data file
a. Research Question: Does the format of delivery (flipped versus traditional) impact student performance on an end of course multiple choice exam?

4) Your assignment submission is a Word document that includes the following:
a. Just the output table that shows the “Independent Samples Test” results
b. Answer the following questions briefly (1-2 sentences max each)

  • Describe each group’s general performance in the test using descriptive statistics – do not make difference claims here, this is reporting of descriptive
    data, just share with us the summarized results
  • Does this analysis violate the assumption of homogeneity of variance? How do you know?
  • What is the actual t-statistic you will report for this analysis with regards to student performance on the multiple choice exam?
  • What is the p-value with regards to student performance on the multiple choice exam?
  • Write up a one-paragraph simple interpretation that summarizes the findings

5) Submit the Word document including your answers to (a) and (b: i-v) to Dropbox by the deadline Challenge Task is not required but you are invited to complete it if you’d like to challenge yourself

Challenge Task: Repeat steps in (4) above for the following second research question: Does format of delivery (flipped versus traditional) impact student performance on an end of course document based essay exam?

Why do you consider them the most innovative works? What about them is innovative? How did they influence later artists? Who were the later artists that they influenced?

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Final

In a 3 page essay, discuss, from your readings, what you consider the three most innovative artworks or buildings from the Prehistoric Period through the Late Gothic / Proto-Renaissance Period (30,000 BCE to the 1300s CE) (chapters 1 through 14 of Gardner’s Art Through the Ages). Your three choices must come from the course textbook and the works we studied in class. You can choose any work from your Homework lists.

Answer the following questions in a well crafted essay (that includes an Introduction, Body and Conclusion).

1) Why do you consider them the most innovative works? What about them is innovative?

2) How did they influence later artists? Who were the later artists that they influenced?

Describe and explain each of your choices fully (including their formal elements). Include specific artists, titles, dates and styles, and use terms from your textbook to illustrate your points.