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Basic Statistics

iStudy would like to acknowledge Jackie Ritzko for revising the content of this tutorial.

Purpose

Statistical terms will play an increasingly important role throughout your college career. Understanding the terms and processes of statistics is necessary for you to understand your own research and the research of other scholars.

Goals and Objectives

Upon completion of this tutorial, you will be able to:

• Define a variety of basic statistical terms and concepts
• Solve fundamental statistical problems
• Use your understanding of statistical fundamentals to interpret data

Activities

Read about mean, median, mode, significant differences, and correlations and complete the activities.

• Definitions of Basic Statistical Terms

• Activity 1: Quiz Yourself on Statistical Terms

• Activity 2: Quiz Yourself About Statistical Calculations

• Activity 3: More about The Three Ms

• Activity 4: Rs, Ps, and Other Things

 Note: All external links in this tutorial will open in a new window or tab.

References

Summary

Instructor's Guide

Definitions of Basic Statistical Terms

N
"N" is usually used to indicate the number of subjects in a study. Example:

If you have 76 participants in a study, N=76.

The Three Ms

Mean

The average result of a test, survey, or experiment.

Example:

Heights of five people: 5 feet 6 inches, 5 feet 7 inches, 5 feet 10 inches, 5 feet 8 inches, 5 feet 8 inches.

The sum is: 339 inches.

Divide 339 by 5 people = 67.8 inches or 5 feet 7.8 inches.

The mean (average) is 5 feet 7.8 inches.

Median

The score that divides the results in half - the middle value.

Examples:

Odd amount of numbers: Find the median of 5 feet 6 inches, 5 feet 7 inches, 5 feet 10 inches, 5 feet 8 inches, 5 feet 8 inches.

Line up your numbers from smallest to largest: 5 feet 6 inches, 5 feet 7 inches, 5 feet 8 inches, 5 feet 8 inches, 5 feet 10 inches.

The median is: 5 feet 8 inches (the number in the middle).

Even amount of numbers: Find the median of 7, 2, 43, 16, 11, 5

Line up your numbers in order: 2, 5, 7, 11, 16, 43

Add the 2 middle numbers and divide by 2: 7 + 11 = 18 ÷ 2 = 9

The median is 9.

Mode

The most common result (the most frequent value) of a test, survey, or experiment.

Example:

Find the mode of 5 feet 6 inches, 5 feet 7 inches, 5 feet 10 inches, 5 feet 8 inches, 5 feet 8 inches.

Put the numbers in order to make it easier to visualize: 5 feet 6 inches, 5 feet 7 inches, 5 feet 8 inches, 5 feet 8 inches, 5 feet 10 inches.

The mode is 5 feet 8 inches (it occurs the most - two times).

Significant Difference

Significance

The measure of whether the results of research were due to chance. The more statistical significance assigned to an observation, the less likely the observation occurred by chance.

p-value

The way in which significance is reported statistically (i.e. p<.01 means that there is a less than 1% chance that the results of a study are due to random chance). Note that in general p-values need to be fairly low (.01 and .05 are common) in order for a study to make any strong claims based on the results.

Example:

• A study had one group of students (Group A) study using notes they took in class; the other group (Group B) studied using notes they took after class using a recording of the lecture. Students in Group A scored higher on a test than Group B. The study reports a significance of p<.01 for the results.
• This means that whatever the reason students who took notes in class did better on the test, there is only a 0 - 1% chance that the results are due to some random factor (such as Group A having smarter students than Group B).

Correlation

Correlation

The degree to which two factors appear to be related. Correlation should not be confused with causation. Just because two factors are reported as being correlated, you cannot say that one factor causes the other. For example, you might find a correlation between going to the library at least 40 times per semester and getting high scores on tests. However, you cannot say from these findings what about going to the library, or what about people who go to libraries often, is responsible for higher test scores.

r-value

The way in which correlation is reported statistically (a number between -1 and +1). Generally, r-values should be >+/-.3 in order to report a significant correlation.

• An r-value of -1 indicates a extreme negative correlation between two variables - as one variable's value tends to increase, the other variable's value tends to decrease.
• An r-value of +1 indicates an extreme positive correlation between two variables - as one variable's value tends to increase, the other variable's value also tends to increase.
• An r-value of 0 means there is no correlation at all between the elements being studied.

Activity 1: Quiz Yourself on Statistical Terms

Check to see what you have learned about statistical terms.

Activity 2: Quiz Yourself About Statistical Calculations

Take the quiz below to see if you understand how to do all of the statistical calculations explained.

Activity 3: More about The Three Ms

Working with central tendencies of data (mean, median, mode) is useful because it makes data more managable. Think of some data you are interested in studying. The temperatures of cities you are considering for a vacation or for relocation could be an example. Which cities have consistent temperatures? Which cities have temperatures that vary greatly over twelve months? How does this statistical data fit into your vacation plans?

List several collections of data that you find interesting. Figure out, make up, or otherwise obtain the details of the data and calculate the mean, median, and mode. Are these three attributes all very similar in value? If so, why do you think this happens? If not, why do you think the attributes vary? Try to collect or build at least one set of data for which the "3 Ms" are dissimilar or "skewed."

Use the following format when listing your collections:

Description of Data:

Values:

Mean:

Median:

Mode:

Analysis:

Note: A downloadable RTF of this activity in the form of a worksheet is included on the left sidebar of this page.

 Show/hide comprehension question...

Activity 4: Rs, Ps, and Other Things

Definitions and examples of r-values and p-values only go so far when understanding these concepts. Familiarity with other common statistical terms will help you as you progress through college. 

Using the library or the Internet, construct your own versions of definitions and examples of r-values and p-values. As you search for more interesting definitions and examples, collect and read an article or research study that uses these terms. As you read the article or study, make a list of four or five other terms that are used. Find definitions and explanations for these also.

For example, look for common terms such as population, sample, regression, and distribution. You might also want to consider terms that you see used in the newspaper or in textbooks that you don't fully understand. Use this as an opportunity to become a more active reader as well as a chance to learn more about basic statistical concepts. 

Then, compare your new definitions and examples with a classmate's or friend's. Are they similar? Do you have a common understanding of these terms? What other terms have you chosen to find and define? Why are they useful?

Use the following format when listing your definitions and examples:

My r-value definition and example:

My p-value definition and example:

Definitions and examples of other statistical terms:

My comparisons:

Note: A downloadable RTF of this activity in the form of a worksheet is included on the left sidebar of this page.

 Show/hide comprehension question...

References

Content

• Burlingame, L. (2002).  Handout on Basic Statistics and Correlations. Retrieved April 1, 2004, from http://lamar.colostate.edu/~bostonlj/documents/basc.pdf *

• Children's Mercy Hospital. (2004). Stats: Definitions of Important Terms. Retrieved April 1, 2004, from http://www.cmh.edu/stats/definitions.asp *

• Dakins, M. (2002). Module 1: Review of Basic Statistical Concepts. Retrieved June 6, 2017, from http://www.webpages.uidaho.edu/envs541/Module_01/module_1.htm

• Hill, J. (2003). Introduction to Descriptive Statistics. Retrieved July 23, 2012, from http://www.mste.uiuc.edu/hill/dstat/dstat.html

• Locke, W. (1998). Basic Statistical Techniques. Retrieved April 1, 2004, from http://www.homepage.montana.edu/~ueswl/topotechs/basic_statistics.htm *

• Marden, J. (1997).  The CUWU (Champaign-Urbana Web University) Statistics Program (2007 version). Retrieved July 23, 2012, from http://www.stat.uiuc.edu/courses/stat100//cuwu/

• Stockburger, D. W. (1996). Introductory statistics: Concepts, Models, and Applications. Retrieved June 6, 2017, from http://www.psychstat.missouristate.edu/introbook/sbk00.htm

• The Shodor Education Foundation, Inc. (1997). Lesson: Statistics and Probability Concepts. Retrieved June 6, 2017, from http://core.ecu.edu/psyc/wuenschk/StatsLessons.htm

 * Indicates that the original Website is no longer available.

Image Credits

U.S. City Statistics

• Source: http://www.davidrumsey.com/luna/servlet/detail/RUMSEY~8~1~20786~560067:Social-statistics-of-22-of-the-larg?sort=Pub_List_No_InitialSort%2CPub_Date%2CPub_List_No%2CSeries_No&qvq=q:social%2Bstatistics;sort:Pub_List_No_InitialSort%2CPub_Date%2CPub_List_No%2CSeries_No;lc:RUMSEY~8~1&mi=0&trs=10

• This file is labeled for reuse in Google Images.

Summary

Mean—The average result of a test, survey, or experiment.

Median—The score that divides the results in half.

Mode—The most common result of a test, survey, or experiment.

Significance—The measure of whether the results of research were due to chance.

p-value—The way in which significance is reported statistically. For example, p<.01 means that there is a less than 1% chance that the results of a study are due to random chance.

Correlation—The degree to which two factors appear to be related.

r-value—The way that correlation is reported statistically. It's a number between –1 and +1. If r=0, there is little or no correlation between two variables. When the number is higher, the positive correlation between two variables is greater. Generally, r-values should be >.3 in order to report a significant positive correlation.

Instructor's Guide

Quizzes, Reflective Questions, and Activities

Following are the assignments embedded in the Basic Statistics tutorial:

• Activity 1: Quiz Yourself about Statistical Terms
• Activity 2: Quiz Yourself on Statistical Calculations
• Activity 3: Worksheet - More Three M's
• Activity 4: Worksheet - R's, P's, and Other Things

Relationship to Other iStudy Tutorials

This tutorial should be used before or in conjunction with the Source Evaluation tutorial, for statistics are one method for evaluating source materials. It can also be used in conjunction with the Oral Presentation tutorial.

Suggested In-class Methods of Presentation

Lecture

• Explain the purpose/intent of the session. Refer to the Purpose section for more detail.
• Explain general information about statistics, and why statistics are important.

Discussion

• Reinforce the basic statistical concepts as listed in the Key Points section below.
• Provide examples of how statistics are used in topics that are relevant to the learners.

OPTIONAL - Have students look in the local or college newspaper for examples of statistics. Have them identify the statistics used.

Note: This is an excellent opportunity to utilize and reinforce the cooperative earning techniques found in the Cooperative Learning tutorial.

Key Points

These points are covered in the iStudy tutorial, but should be emphasized in any discussions.

• Mean, median, and mode
• Separate symptoms from causes (significance, P value)
• Define and analyze the problem (correlation, r value)

Assessment Criteria

Through observing both the group's and the individuals' activities, the instructor may assess student performance. Assessment criteria are as follows (instructors supply the percentage weights):