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.
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.
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
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
Subscripts serve to differentiate one value from another and that they are not the same:
S_{x} – a value for sample x
S_{y} – 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
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
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.
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
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
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