Statistics for the Behavioral Sciences

Lesson 1

Introduction to Statistics

Roger N. Morrissette, PhD

 


I. An Introduction to Statistics

  Statistics is a branch of applied mathematics that psychologists use to plan research; to gather, organize and analyze data; to present data in research papers; and to make inferences about data. Ultimately, psychologists use statistics to support or refute predictions concerning the behavior of humans and non-human animals.


II. Statistics and Math Anxiety

  Mathematical formulas are no more difficult than those in basic algebra. A more difficult part of statistics are the concepts, the reasons for doing certain operations, and the logic behind the computations.


III. Features of the Book

 

                Chapter Outline

                Chapter Opener

                Student Questions

                Concept Quizzes

                Chapter Summary

                Key Terms

                Formulas

                Problems

 

                Course and Book Goal:

 

1.        to teach you the mathematical formulas for computing statistics

2.        to teach you the logic underlying the computation and use of those statistics

 


IV. Tips for Doing Well in Statistics, or How to Succeed in Statistics by Really Trying

 

1.        Statistics is cumulative

2.        Your professor is there to help

3.        Make friends quickly

always have a pencil, paper, and calculator handy when starting a new chapter

work on all the numerical examples in the text

4.        Practice helps

5.        Calculators are necessary

calculator must do addition, subtraction, multiplication, division, and square roots

6.        Get a “feel” for statistics

try to understand the concepts behind the formulas

e.g., scientists never “prove” anything

determine whether each sum or statistic is logical

  


V. A Note About Notation and Rounding

 

                Subscripts serve to differentiate one value from another and that they are not the same:

                                Sx – a value for sample x

                                Sy – a value for sample y

 

                We will be rounding to the nearest thousands (or to three decimal places).

                                ignore any decimal point after 4

                                5 or greater is rounded up

                                                2.9985547786

2.999

                                4 or less is rounded down

                                                5.8544998482

5.854

                               


VI. Hypotheses

 

                A Hypothesis is a possible explanation for the behavior being studied that is based on previously gathered facts and theories. It is expressed as a prediction. A Scientific Hypothesis is not always true, but it is stated in such a way that it can be proved false if indeed it is false.

 

                research hypothesis

                                one that the researcher wishes to support

                                           e.g.: Chronic use of MDMA (ecstasy) causes brain damage

 

                null hypothesis

                                one the research wants to reject because it proposes that there will be no change in behavior, no difference between the groups being measured.

                                                it is the null hypothesis that is tested in a research study

                                           e.g.: Chronic use of MDMA (ecstasy) no change in the brain 

                                 


VII. Variables

  In an Experiment the scientist must hold everything constant except for the factor being investigated. In this way he or she can attribute any change in behavior directly to the factors being manipulated, since all other factors have been held constant.

          Variables are events or qualities that “vary.” They can assume more than one value.

 

                    Independent Variable is a factor that is selected and manipulated, or controlled by the experimenter. It is totally independent of anything the subject does.

               

                    Dependent Variable is a measurable behavior exhibited by the subject. The dependent variable "depends" on the independent variable.

 

                    Extraneous (or Confounding) Variables are “extra” variables that may affect the outcome of the experiment but are not directly related to the study.

 


VIII. Scales of Measurement

 

               All data that is collected is on one of four measurement scales:

 

1. Nominal Scale

used for qualitative data

                e.g., gender, personality type, Yes/No, A/B

                                               

                                2. Ordinal Scale

                                                used for data that will be simply ranked from highest to lowest

                                                tells us the relative difference between ranks

                                                but not the specific difference or how different the rankings are

 

                                “Continuous”

                                                can take an average (mean) of the values

                                

                                3. Interval Scale

                                                  indicates relative rank AND equal distances between the ranks

                                                  but does not have a true zero

                                                  a point at which there is a total absence of the variable being measured

                                                  can not make ratio type comparisons

                                                      e.g., an 80 IQ is not half as a 160 IQ

                                                      e.g., you can not have an IQ of 0

 

                                         4. Ratio Scale

                                                   indicates relative rank AND equal distances between the ranks

                                                   AND has a relative zero point

                                                   a point at which there is a total absence of the variable being measured

 


IX. Populations and Samples

 

                The purpose of psychological inquiry is to determine how everyone should behave in a given situation.

 

                Population (N):

                                includes all members of a certain group.

                                can be large or small

                                must contain all of the members

 

                Sample (n):

                                a relatively small representative group selected from a population

                                research is typically done with a small sample of the population due to time and money

                                results are then generalized to a larger population

 

                Parameters:

                                describe population values

                                                e.g., mean

 

                Estimates:

                                statistics collected from samples that describe population values