The Study of Quantitative Methods

… a core topic in Quantitative Methods and Atlas104

StatisticsTopicTopic description

This topic introduces students to the study of quantitative methods and some of the key terms.

The treatment of this topic on the Atlas follows almost precisely that in Chapter I, Introduction, of OnlineStatBook, Online Statistics Education – An Interactive Multimedia Course of Study, at http://onlinestatbook.com/2/introduction/introduction.html, accessed 13 May 2016.

Topic learning outcome

Familiarity with the general purpose and nature of quantitative methods including following core concepts and terms.

[Note: Until Atlas pages are created for individual concepts in Quantitative Methods, the links in the concepts below point directly to the relevant pages in OnlineStatBook.]

Core concepts associated with this topic
What are Statistics?

Importance of Statistics

Descriptive Statistics

Inferential Statistics

Variables

Percentiles

Levels of Measurement

Distributions

Power Laws, Pareto Distributions, and Performance

Summation Notation

Linear Transformations

Logarithms

Readings

Read and/or watch video for each of the concept pages above (top to bottom, starting in left column).

Read the Statistical Literacy exercises, Do Athletes Get Special Treatment? and Statistical Errors in Politics, and answer the questions.

Read the Angry Moods (AM) case study and complete following exercises:

  • Which variables are the participant variables? (They act as independent variables in this study.) (relevant section)
  • What are the dependent variables? (relevant section)
  • Is Anger-Out a quantitative or qualitative variable? (relevant section)

Read the Teacher Ratings (TR) case study and complete following exercise:

Read the ADHD Treatment (AT) case study and complete the following exercises:

  • What is the independent variable of this experiment? How many levels does it have? (relevant section)
  • What is the dependent variable? On what scale (nominal, ordinal, interval, ratio) was it measured? (relevant section)

Assessment questions

From http://onlinestatbook.com/2/introduction/ch1_exercises.html#casestudies, accessed 14 May 2016.

AQ104.01.01. A teacher wishes to know whether the males in his/her class have more conservative attitudes than the females. A questionnaire is distributed assessing attitudes and the males and the females are compared. Is this an example of descriptive or inferential statistics? (relevant section 1, relevant section 2)

AQ104.01.02. A cognitive psychologist is interested in comparing two ways of presenting stimuli on subsequent memory. Twelve subjects are presented with each method and a memory test is given. What would be the roles of descriptive and inferential statistics in the analysis of these data? (relevant section 1 & relevant section 2)

AQ104.01.03. If you are told that you scored in the 80th percentile, from just this information would you know exactly what that means and how it was calculated? Explain. (relevant section)

AQ104.01.04. A study is conducted to determine whether people learn better with spaced or massed practice. Subjects volunteer from an introductory psychology class. At the beginning of the semester 12 subjects volunteer and are assigned to the massed-practice condition. At the end of the semester 12 subjects volunteer and are assigned to the spaced-practice condition. This experiment involves two kinds of non-random sampling: (1) Subjects are not randomly sampled from some specified population and (2) Subjects are not randomly assigned to conditions. AQ104.01.04.1 Which of the problems relates to the generality of the results? AQ104.01.04.2 Which of the problems relates to the validity of the results? AQ104.01.04.3 Which problem is more serious? (relevant section)

AQ104.01.05. Give an example of an independent and a dependent variable. (relevant section)

AQ104.01.06. Categorize the following variables as being qualitative or quantitative: (relevant section)

Rating of the quality of a movie on a 7-point scale
Age
Country you were born in
Favorite Color
Time to respond to a question

AQ104.01.07. Specify the level of measurement used for the items in AQ104.01.06. (relevant section)

AQ104.01.08. Which of the following are linear transformations? (relevant section)

Converting from meters to kilometers
Squaring each side to find the area
Converting from ounces to pounds
Taking the square root of each person’s height.
Multiplying all numbers by 2 and then adding 5
Converting temperature from Fahrenheit to Centigrade.

AQ104.01.09. The formula for finding each student’s test grade (g) from his or her raw score (s) on a test is as follows: g = 16 + 3s

AQ104.01.09.1 Is this a linear transformation? AQ104.01.09.2 If a student got a raw score of 20, what is his test grade? (relevant section)

AQ104.01.10. For the numbers 1, 2, 4, 16, compute the following: (relevant section)

AQ104.01.10.1 ΣX
AQ104.01.10.2 ΣX2
AQ104.01.10.3 (ΣX)2

AQ104.01.11.1 Which of the frequency polygons has a large positive skew? AQ104.01.11.2 Which has a large negative skew? (relevant section)

AQ104.01.12. What is more likely to have a skewed distribution: time to solve an anagram problem (where the letters of a word or phrase are rearranged into another word or phrase like “dear” and “read” or “funeral” and “real fun”) or scores on a vocabulary test? (relevant section)

Questions from Case Studies:

The following questions are from the Angry Moods (AM) case study.

AQ104.01.13. (AM#1) Which variables are the participant variables? (They act as independent variables in this study.) (relevant section)

AQ104.01.14. (AM#2) What are the dependent variables? (relevant section)

AQ104.01.15. (AM#3) Is Anger-Out a quantitative or qualitative variable? (relevant section)

The following question is from the Teacher Ratings (TR) case study.

AQ104.01.16. (TR#1) What is the independent variable in this study? (relevant section)

The following questions are from the ADHD Treatment (AT) case study.

AQ104.01.17.1 (AT#1) What is the independent variable of this experiment? AQ104.01.17.2 How many levels does it have? (relevant section)

AQ104.01.18. (AT#2) What is the dependent variable? On what scale (nominal, ordinal, interval, ratio) was it measured? (relevant section)

Page created by: Ian Clark, last modified on 11 June 2017.

Image: University of Virginia, StatLab, at http://data.library.virginia.edu/statlab/, accessed 14 May 2016.