SUMMARY STATISTICS FOR THE
BEHAVIORAL SCIENCES
Gregory J. Privitera
Second edition
Year: 2019/2020
CM1005
,Table of contents
Chapter 1: Introduction to statistics............................................................................................................... 3
Chapter 3: Summarizing data: central tendency.............................................................................................5
Chapter 4: Summarizing data: variability........................................................................................................ 8
Chapter 6: Probability, normal distributions, and Z scores............................................................................13
Chapter 7: Probability and sampling distributions........................................................................................15
Chapter 8: Hypothesis testing: significance, effect size, and power...............................................................18
Chapter 9: Testing means: one-sample and two-independent-sample t tests................................................21
Chapter 11: Estimation and confidence intervals..........................................................................................23
Chapter 12: Analysis of variance: one way between subjects design.............................................................25
Chapter 15: Correlation................................................................................................................................ 29
Chapter 16: Linear regression and multiple regression..................................................................................31
Chapter 17: nonparametric tests: chi-square tests........................................................................................32
,Chapter 1: Introduction to statistics
Statistics = a branch of mathematics used to summarize, analyze, and interpret what
we observe – to make sense or meaning of our observations. Really, statistics is used to
make sense of the observations we make.
Descriptive statistics = procedures used to summarize, organize and make sense of a
set of scores or observations. Descriptive statistics are typically presented graphically, in
tabular form or as summary statistics. Are typically used to quantify the behaviors
researchers measure.
Inferential statistics = procedures used to allow researchers to infer or generalize
observations made with samples to the larger population from which they were selected.
Descriptive statistics applying statistics to organize and summarize information
Inferential statistics applying statistics to interpret the meaning of information
Data = the recorded observations that researchers make.
General structure for making scientific observations
1. Ask a question
2. Set up a research study
3. Evaluate findings
4. Measure behavior
Mean = average
Median = middle
Mode = common
Tables and graphs serve a similar purpose to summarize large and small sets of data.
One particular advantage of tables and graphs is that they can clarify findings in a
research study.
Population = the set of all individuals items, or data of interest. This is the group about
which scientists will generalize
Population parameter = a characteristic (usually numeric) that describes a population
Sample = a set of individuals, items, or data selected from a population of interest
Sample statistic = a characteristic (usually numeric) that describes a sample. This is
the value that is measured in the study. A sample statistic is measured to estimate the
population parameter.
1.4 Scales of measurement
in all, scales of measurement are characterized by 3 properties:
1. Order: does a larger number indicate a greater value than a smaller number?
2. Difference: does subtracting two numbers represent some meaningful value?
3. Ratio: does dividing two
numbers represent some
meaningful value?
Scales of measurement = rules
for how the properties of numbers
can change with different uses
, - Nominal scales: measurements in which a number is assigned to represent
something or someone
- Ordinal scales: measurements that convey order or rank alone
- Interval scales: measurements that have no true zero and are distributed in equal
units
- Ratio scales: measurements that have a true zero and are distributed in equal
units
Coding = the procedure of converting a nominal or categorical variable to a numeric
value
true zero = when the value 0 truly indicates nothing on a scale of measurement.
Interval scales do not have a true zero
researchers also distinguish between the types of data they measure. The variables for
which researchers measure data fall into two broad categories:
- Variables can be categorized as continuous or discrete
- Variables van be categorized as quantitative or qualitative
Continuous variable = is measured along a continuum at any place beyond the
decimal point. A continuous variable can thus be measured in fractional units e.g. time for
Olympic sprinters
Discrete variable = is measured in whole units or categories that are not distributed
along a continuum e.g. number of brothers and sisters
Quantitative variable = varies by amount. This variable is measured numerically and is
often collected by measuring or counting
Qualitative variable = varies by class. This variable is often represented as a label and
describes nonnumeric aspects of phenomena (only discrete variables).
BEHAVIORAL SCIENCES
Gregory J. Privitera
Second edition
Year: 2019/2020
CM1005
,Table of contents
Chapter 1: Introduction to statistics............................................................................................................... 3
Chapter 3: Summarizing data: central tendency.............................................................................................5
Chapter 4: Summarizing data: variability........................................................................................................ 8
Chapter 6: Probability, normal distributions, and Z scores............................................................................13
Chapter 7: Probability and sampling distributions........................................................................................15
Chapter 8: Hypothesis testing: significance, effect size, and power...............................................................18
Chapter 9: Testing means: one-sample and two-independent-sample t tests................................................21
Chapter 11: Estimation and confidence intervals..........................................................................................23
Chapter 12: Analysis of variance: one way between subjects design.............................................................25
Chapter 15: Correlation................................................................................................................................ 29
Chapter 16: Linear regression and multiple regression..................................................................................31
Chapter 17: nonparametric tests: chi-square tests........................................................................................32
,Chapter 1: Introduction to statistics
Statistics = a branch of mathematics used to summarize, analyze, and interpret what
we observe – to make sense or meaning of our observations. Really, statistics is used to
make sense of the observations we make.
Descriptive statistics = procedures used to summarize, organize and make sense of a
set of scores or observations. Descriptive statistics are typically presented graphically, in
tabular form or as summary statistics. Are typically used to quantify the behaviors
researchers measure.
Inferential statistics = procedures used to allow researchers to infer or generalize
observations made with samples to the larger population from which they were selected.
Descriptive statistics applying statistics to organize and summarize information
Inferential statistics applying statistics to interpret the meaning of information
Data = the recorded observations that researchers make.
General structure for making scientific observations
1. Ask a question
2. Set up a research study
3. Evaluate findings
4. Measure behavior
Mean = average
Median = middle
Mode = common
Tables and graphs serve a similar purpose to summarize large and small sets of data.
One particular advantage of tables and graphs is that they can clarify findings in a
research study.
Population = the set of all individuals items, or data of interest. This is the group about
which scientists will generalize
Population parameter = a characteristic (usually numeric) that describes a population
Sample = a set of individuals, items, or data selected from a population of interest
Sample statistic = a characteristic (usually numeric) that describes a sample. This is
the value that is measured in the study. A sample statistic is measured to estimate the
population parameter.
1.4 Scales of measurement
in all, scales of measurement are characterized by 3 properties:
1. Order: does a larger number indicate a greater value than a smaller number?
2. Difference: does subtracting two numbers represent some meaningful value?
3. Ratio: does dividing two
numbers represent some
meaningful value?
Scales of measurement = rules
for how the properties of numbers
can change with different uses
, - Nominal scales: measurements in which a number is assigned to represent
something or someone
- Ordinal scales: measurements that convey order or rank alone
- Interval scales: measurements that have no true zero and are distributed in equal
units
- Ratio scales: measurements that have a true zero and are distributed in equal
units
Coding = the procedure of converting a nominal or categorical variable to a numeric
value
true zero = when the value 0 truly indicates nothing on a scale of measurement.
Interval scales do not have a true zero
researchers also distinguish between the types of data they measure. The variables for
which researchers measure data fall into two broad categories:
- Variables can be categorized as continuous or discrete
- Variables van be categorized as quantitative or qualitative
Continuous variable = is measured along a continuum at any place beyond the
decimal point. A continuous variable can thus be measured in fractional units e.g. time for
Olympic sprinters
Discrete variable = is measured in whole units or categories that are not distributed
along a continuum e.g. number of brothers and sisters
Quantitative variable = varies by amount. This variable is measured numerically and is
often collected by measuring or counting
Qualitative variable = varies by class. This variable is often represented as a label and
describes nonnumeric aspects of phenomena (only discrete variables).
