Summary IOBO
Statistics for the behavioural sciences
Chapter 1: introduction to statistics
-statistics consists of facts and figures
*they are usually informative and time-saving because they condense large quantities of
information into a few simple figures
-statistics have two general purposes
*to organize and summarize the information so that the researcher can see what happened
in the research study and can communicate the results to others
*help the researcher to answer the questions that initiated the research by determining
exactly what general conclusions are justified based on the specific results that were
obtained
-statistics= a set of mathematical procedures for organizing, summarizing, and interpreting
information
-population= the set of all the individuals of interest in a particular study
-the researcher always needs to identify the population being studied
-sample= a set of individuals selected from a population, usually intended to represent the
population in a research study
*when the population as a whole is too big to study
*afterwards the results need to be generalized
-variable= a characteristic or condition that changes or has different values for different
individuals
-data= measurements or observations
-data set= a collection of measurements or observations
-datum= a single measurement or observation and is commonly called a score or raw score
-parameter= a value that describes a population
-statistic= a value that describes a sample
-descriptive statistics= statistical procedures used to summarize, organize, and simplify data
-inferential statistics= consists of techniques that allow us to study samples and then make
generalizations about the populations form which they were selected
-a sample only provides limited information about the population
*there is usually a discrepancy between a sample statistic and the corresponding
population parameter
>this is called the sampling error
-sampling error= the naturally occurring discrepancy, or error, that exists between a sample
statistic and the corresponding population parameter
-two methods for examining the relationship between variables:
*the correlation method= two different variables are observed to determine whether there
is a relationship between them
>observing the two variables as they exist naturally for a set of individuals (measure the
two variables for each individual)
, >this method does not provide an explanation for the relationship
*(non) experimental method
>comparison of two or more groups of scores
>using one of the variables to define the groups, then measuring the second variable to
obtain scores for each group
>experimental method
^the results from an experiment allow a cause-and-effect explanation
^manipulation= the researcher manipulates one variable by changing its value from one
level to another
^control= the researcher must exercise control over the research situation to ensure that
other, extraneous variables do no influence the relationship being examined
^participant variables= characteristics such as age and gender that vary from one
individual to another
^environmental variables= characteristics of the environment such as lighting and
Weather
^independent variable= the variable that is manipulated by the researcher (it usually has
an antecedent that was manipulated prior to observing)
^dependent variable= the one that is observed to assess the effect of the treatment
^experimental method= one variable is manipulated while another variable is observed
and measured. To establish a cause-and-effect relationship
>nonexperimental method
^a nonexperimental study does not permit a cause-and-effect explanation
^research designs that are not true experiments but still examine the relationship
between variables by comparing groups of scores
^quasi-independent variable= the independent variable that is used to create different
groups of scores
-scatterplot= each individual is represented by a point
-confounded= whenever a research study allows more than ones explanation for the results
-3 techniques to control other variables
1. random assignment (each participant has an equal chance of being assigned to each
of the treatment conditions)
2. matching (to ensure equivalent groups)
3. holding them constant
-control condition= individuals in this do not receive the experimental treatment (either no
treatment or placebo etc.), the purpose is to provide a baseline for comparison
-experimental condition= individuals in this to receive the experimental treatment
-constructs= internal attributes or characteristics that cannot be directly observed but are
useful for describing and explaining behaviour
-an operational definition= identifies a measurement procedure for measuring an external
behaviour and uses the resulting measurements as a definition and a measurement of a
hypothetical construct
-discrete variable= consists of separate, indivisible categories. No values can exist between
two neighbouring categories
-continuous variable= has an infinite number of possible values that fall between any two
observed values. A continuous variable is divisible into an infinite number of fractional parts
-real limits= the boundaries of intervals for scores that are represented on a continuous
, number line. The real limit separating two adjacent scores is located exactly halfway
between the scores. Each score has two real limits. The upper real limit is at the top of the
interval, and the lower limit is at the bottom
-the categories used to measure a variable make up a scale of measurement
-measurement on a nominal scale involves classifying individuals into categories that have
different names but are not related to each other in any systematic way
-nominal scale= consists of a set of categories that have different names. Measurements on
a nominal scale label and categorize observations, but do not make any quantitative
distinctions between observations
-ordinal scale= consists of a set of categories that are organized in an ordered sequence.
Measurements on an ordinal scale, rank observations in terms of size or magnitude
-interval scale= consists of ordered categories that are all intervals of exactly the same size.
Equal differences between numbers on scale reflect equal differences in magnitude.
However, the zero point on an interval scale is arbitrary and does not indicate a zero
amount of the variable being measured
-ratio scale= an interval scale with the additional feature of an absolute zero point. With a
ratio scale, ratios of numbers do reflect ratios of magnitude
-raw scores are the original, unchanged scores obtained in the study
-X= scores for a particular variable (and Y when two)
-N= used to specify how many scores are in a set
*N= is in a population
*n= in a sample
-= summation
-X= summation of all the scores for X
Chapter 2: frequency distributions
-frequency distribution= an organized tabulation of the number of individuals located in
each category on the scale of measurement
*2 elements
>the set of categories that make up the original measurement scale
>a record of the frequency, or number of individuals in each category
-proportion is p= f/N
-grouped frequency distribution table= presenting groups of scores
-apparent limits= upper and lower boundaries for the class interval (40-49: X=40 to X=49)
-when the date is measured on an interval or ratio scale there are two options for a
frequency distribution graph:
*histograms
*polygons
-the midpoint is the lowest point plus the highest point divided by 2
-when the date is measured on a nominal or ordinal scale the frequency distribution can be
displayed in a:
*bar graph
-relative frequency (when exact numbers are not known)
Statistics for the behavioural sciences
Chapter 1: introduction to statistics
-statistics consists of facts and figures
*they are usually informative and time-saving because they condense large quantities of
information into a few simple figures
-statistics have two general purposes
*to organize and summarize the information so that the researcher can see what happened
in the research study and can communicate the results to others
*help the researcher to answer the questions that initiated the research by determining
exactly what general conclusions are justified based on the specific results that were
obtained
-statistics= a set of mathematical procedures for organizing, summarizing, and interpreting
information
-population= the set of all the individuals of interest in a particular study
-the researcher always needs to identify the population being studied
-sample= a set of individuals selected from a population, usually intended to represent the
population in a research study
*when the population as a whole is too big to study
*afterwards the results need to be generalized
-variable= a characteristic or condition that changes or has different values for different
individuals
-data= measurements or observations
-data set= a collection of measurements or observations
-datum= a single measurement or observation and is commonly called a score or raw score
-parameter= a value that describes a population
-statistic= a value that describes a sample
-descriptive statistics= statistical procedures used to summarize, organize, and simplify data
-inferential statistics= consists of techniques that allow us to study samples and then make
generalizations about the populations form which they were selected
-a sample only provides limited information about the population
*there is usually a discrepancy between a sample statistic and the corresponding
population parameter
>this is called the sampling error
-sampling error= the naturally occurring discrepancy, or error, that exists between a sample
statistic and the corresponding population parameter
-two methods for examining the relationship between variables:
*the correlation method= two different variables are observed to determine whether there
is a relationship between them
>observing the two variables as they exist naturally for a set of individuals (measure the
two variables for each individual)
, >this method does not provide an explanation for the relationship
*(non) experimental method
>comparison of two or more groups of scores
>using one of the variables to define the groups, then measuring the second variable to
obtain scores for each group
>experimental method
^the results from an experiment allow a cause-and-effect explanation
^manipulation= the researcher manipulates one variable by changing its value from one
level to another
^control= the researcher must exercise control over the research situation to ensure that
other, extraneous variables do no influence the relationship being examined
^participant variables= characteristics such as age and gender that vary from one
individual to another
^environmental variables= characteristics of the environment such as lighting and
Weather
^independent variable= the variable that is manipulated by the researcher (it usually has
an antecedent that was manipulated prior to observing)
^dependent variable= the one that is observed to assess the effect of the treatment
^experimental method= one variable is manipulated while another variable is observed
and measured. To establish a cause-and-effect relationship
>nonexperimental method
^a nonexperimental study does not permit a cause-and-effect explanation
^research designs that are not true experiments but still examine the relationship
between variables by comparing groups of scores
^quasi-independent variable= the independent variable that is used to create different
groups of scores
-scatterplot= each individual is represented by a point
-confounded= whenever a research study allows more than ones explanation for the results
-3 techniques to control other variables
1. random assignment (each participant has an equal chance of being assigned to each
of the treatment conditions)
2. matching (to ensure equivalent groups)
3. holding them constant
-control condition= individuals in this do not receive the experimental treatment (either no
treatment or placebo etc.), the purpose is to provide a baseline for comparison
-experimental condition= individuals in this to receive the experimental treatment
-constructs= internal attributes or characteristics that cannot be directly observed but are
useful for describing and explaining behaviour
-an operational definition= identifies a measurement procedure for measuring an external
behaviour and uses the resulting measurements as a definition and a measurement of a
hypothetical construct
-discrete variable= consists of separate, indivisible categories. No values can exist between
two neighbouring categories
-continuous variable= has an infinite number of possible values that fall between any two
observed values. A continuous variable is divisible into an infinite number of fractional parts
-real limits= the boundaries of intervals for scores that are represented on a continuous
, number line. The real limit separating two adjacent scores is located exactly halfway
between the scores. Each score has two real limits. The upper real limit is at the top of the
interval, and the lower limit is at the bottom
-the categories used to measure a variable make up a scale of measurement
-measurement on a nominal scale involves classifying individuals into categories that have
different names but are not related to each other in any systematic way
-nominal scale= consists of a set of categories that have different names. Measurements on
a nominal scale label and categorize observations, but do not make any quantitative
distinctions between observations
-ordinal scale= consists of a set of categories that are organized in an ordered sequence.
Measurements on an ordinal scale, rank observations in terms of size or magnitude
-interval scale= consists of ordered categories that are all intervals of exactly the same size.
Equal differences between numbers on scale reflect equal differences in magnitude.
However, the zero point on an interval scale is arbitrary and does not indicate a zero
amount of the variable being measured
-ratio scale= an interval scale with the additional feature of an absolute zero point. With a
ratio scale, ratios of numbers do reflect ratios of magnitude
-raw scores are the original, unchanged scores obtained in the study
-X= scores for a particular variable (and Y when two)
-N= used to specify how many scores are in a set
*N= is in a population
*n= in a sample
-= summation
-X= summation of all the scores for X
Chapter 2: frequency distributions
-frequency distribution= an organized tabulation of the number of individuals located in
each category on the scale of measurement
*2 elements
>the set of categories that make up the original measurement scale
>a record of the frequency, or number of individuals in each category
-proportion is p= f/N
-grouped frequency distribution table= presenting groups of scores
-apparent limits= upper and lower boundaries for the class interval (40-49: X=40 to X=49)
-when the date is measured on an interval or ratio scale there are two options for a
frequency distribution graph:
*histograms
*polygons
-the midpoint is the lowest point plus the highest point divided by 2
-when the date is measured on a nominal or ordinal scale the frequency distribution can be
displayed in a:
*bar graph
-relative frequency (when exact numbers are not known)
