Appendix A : Statistical Tools for Answering Research Questions
Chapter Outline
What is Your Plan?
Is Our Goal to Describe the Data or to Make Inferences?
What Measurement Scale Are We Using?
How Often Do We Measure Each Participant?
How Many Comparison Groups Does the Study Have?
Choosing the Right Statistical Test for Your Research Design
Descriptive Statistics: Tell Me About My Data
Creating a “Picture” of Our Data
Measuring Central Tendency
Measuring the Variability of the Data
Measuring Associations Between Variables.
Inferential Statistics: Going Beyond Our Sample
Understanding the Logic Behind Statistical Hypothesis Testing
Identifying Potential Errors in Statistical Hypothesis Testing
Measuring the Size of the Effect
Final Thoughts
Chapter learning outcomes:
None
Chapter Concept Guide
Concept Alternate Example
wording
alternative This is A researcher is testing whether the
hypothesis hypothesis that mean self-confidence scores are
is compared to different between two groups. The
the null null hypothesis is that there is no
hypothesis in difference. If the test is statistically
tests of significant the null hypothesis can
statistical be rejected, and the alternative
significance. hypothesis, that there is a
difference between the groups, can
be accepted.
beta (β) The probability A researcher compares two means
of accepting the and finds no difference. She knows
, null hypothesis her statistical power is .95 and
when it is false that β is therefore .05.
(Type II error)
also known as β.
This can be
computed by
subtracting the
statistical power
of a test from
1.0.
Cohen’s d A method for A researcher compares the means
determining the of two conditions in her experiment
size of an and finds a Cohen’s d = 80. This
experimental indicates a large effect size means
effect based on the difference between the means
the is, on average, 80% of a standard
standardized deviation.
difference
between the
means of two
conditions.
dichotomous A measurement A researcher chooses two
variable variable with categories for their independent
only two variable, treatment and control.
mutually
exclusive
categories.
dummy coding When a A researcher may code all male
researcher using participants with a “1” and all
numbers female participants with a “2.”
instead of words
to identify
different levels
of a nominal
variable.
effect size The effect size, r, A researcher computes a point bi-
is the serial correlation between their
correlation independent variable and their
between the dependent variable and finds r =
independent .50. She concludes that there is a
variable and the moderate effect of the independent
dependent variable on the dependent variable.
variable and can
range from 0 (no
effect) to 1.0
, (perfect
correlation).
frequency A method for A researcher may plot the
polygon illustrating data frequency of a behavior on the y-
where a line is axis and the age group of the child
drawn on the x-axis and join the points
connecting the together with a line to form a
values of frequency polygon.
continuous
variables.
histogram A method that A researcher may plot the
uses vertical frequency of a behavior on the y-
bars to illustrate axis and the age group of the child
the values of on the x-axis and use bars to
continuous represent the frequency of behavior
variables. by age group.
interval scale A measurement A researcher measures intelligence
scale which using an IQ test.
assigns
numbers to
categories and
assumes that
there is a
consistent
underlying scale
such that a
difference of two
numbers
represents the
same difference
in the variable
no matter how
large or small
the number is.
measurement The classification A researcher may use a nominal,
scale system being used ordinal, interval or ratio scale in
to assign a order to assign categories to their
measurement to a variables.
variable.
nominal scale A measurement A researcher categorizes
scale consisting participants as “male’ or ‘female.”
of category
names.
normal A data IQ scores fall into a normal
distribution distribution that distribution when plotted for a
, is symmetrical whole population.
around the
mean.
ordinal scale A measurement A researcher assigns a “1” to the
scale that participant with the largest social
involves the network, a “2” to the participant
rank ordering of with the second largest social
categories. network and so on.
Pearson product A correlation A researcher computes the
moment coefficient that correlation between height and
correlation can be weight and finds r = .89 meaning
coefficient computed when that there is a strong positive
(Pearson r) two variables correlation between height and
are continuous. weight in this sample.
p-value The probability A researcher computes a statistic
that the comparing two means and the
difference in the statistic indicates that the means
means is the are different with p < .05, the p-
result of random value is .05.
variation and
not the
experimental
manipulation
represented by
p.
range The difference If the lowest IQ score in the dataset
between the is 80 and the highest is 140 the
lowest score in range for this data set is 60.
the data set and
the highest
score in a data
set.
ratio scale A measurement A psychologist counts the number
scale that of times a child interacts with a
includes a true peer during a period of observation
zero point and and uses this count as the
where equal dependent variable.
differences in
numbers
represent equal
differences in
the variable
being measured.
significance level The probability A researcher finds a difference
of rejecting the between groups with a significance
Chapter Outline
What is Your Plan?
Is Our Goal to Describe the Data or to Make Inferences?
What Measurement Scale Are We Using?
How Often Do We Measure Each Participant?
How Many Comparison Groups Does the Study Have?
Choosing the Right Statistical Test for Your Research Design
Descriptive Statistics: Tell Me About My Data
Creating a “Picture” of Our Data
Measuring Central Tendency
Measuring the Variability of the Data
Measuring Associations Between Variables.
Inferential Statistics: Going Beyond Our Sample
Understanding the Logic Behind Statistical Hypothesis Testing
Identifying Potential Errors in Statistical Hypothesis Testing
Measuring the Size of the Effect
Final Thoughts
Chapter learning outcomes:
None
Chapter Concept Guide
Concept Alternate Example
wording
alternative This is A researcher is testing whether the
hypothesis hypothesis that mean self-confidence scores are
is compared to different between two groups. The
the null null hypothesis is that there is no
hypothesis in difference. If the test is statistically
tests of significant the null hypothesis can
statistical be rejected, and the alternative
significance. hypothesis, that there is a
difference between the groups, can
be accepted.
beta (β) The probability A researcher compares two means
of accepting the and finds no difference. She knows
, null hypothesis her statistical power is .95 and
when it is false that β is therefore .05.
(Type II error)
also known as β.
This can be
computed by
subtracting the
statistical power
of a test from
1.0.
Cohen’s d A method for A researcher compares the means
determining the of two conditions in her experiment
size of an and finds a Cohen’s d = 80. This
experimental indicates a large effect size means
effect based on the difference between the means
the is, on average, 80% of a standard
standardized deviation.
difference
between the
means of two
conditions.
dichotomous A measurement A researcher chooses two
variable variable with categories for their independent
only two variable, treatment and control.
mutually
exclusive
categories.
dummy coding When a A researcher may code all male
researcher using participants with a “1” and all
numbers female participants with a “2.”
instead of words
to identify
different levels
of a nominal
variable.
effect size The effect size, r, A researcher computes a point bi-
is the serial correlation between their
correlation independent variable and their
between the dependent variable and finds r =
independent .50. She concludes that there is a
variable and the moderate effect of the independent
dependent variable on the dependent variable.
variable and can
range from 0 (no
effect) to 1.0
, (perfect
correlation).
frequency A method for A researcher may plot the
polygon illustrating data frequency of a behavior on the y-
where a line is axis and the age group of the child
drawn on the x-axis and join the points
connecting the together with a line to form a
values of frequency polygon.
continuous
variables.
histogram A method that A researcher may plot the
uses vertical frequency of a behavior on the y-
bars to illustrate axis and the age group of the child
the values of on the x-axis and use bars to
continuous represent the frequency of behavior
variables. by age group.
interval scale A measurement A researcher measures intelligence
scale which using an IQ test.
assigns
numbers to
categories and
assumes that
there is a
consistent
underlying scale
such that a
difference of two
numbers
represents the
same difference
in the variable
no matter how
large or small
the number is.
measurement The classification A researcher may use a nominal,
scale system being used ordinal, interval or ratio scale in
to assign a order to assign categories to their
measurement to a variables.
variable.
nominal scale A measurement A researcher categorizes
scale consisting participants as “male’ or ‘female.”
of category
names.
normal A data IQ scores fall into a normal
distribution distribution that distribution when plotted for a
, is symmetrical whole population.
around the
mean.
ordinal scale A measurement A researcher assigns a “1” to the
scale that participant with the largest social
involves the network, a “2” to the participant
rank ordering of with the second largest social
categories. network and so on.
Pearson product A correlation A researcher computes the
moment coefficient that correlation between height and
correlation can be weight and finds r = .89 meaning
coefficient computed when that there is a strong positive
(Pearson r) two variables correlation between height and
are continuous. weight in this sample.
p-value The probability A researcher computes a statistic
that the comparing two means and the
difference in the statistic indicates that the means
means is the are different with p < .05, the p-
result of random value is .05.
variation and
not the
experimental
manipulation
represented by
p.
range The difference If the lowest IQ score in the dataset
between the is 80 and the highest is 140 the
lowest score in range for this data set is 60.
the data set and
the highest
score in a data
set.
ratio scale A measurement A psychologist counts the number
scale that of times a child interacts with a
includes a true peer during a period of observation
zero point and and uses this count as the
where equal dependent variable.
differences in
numbers
represent equal
differences in
the variable
being measured.
significance level The probability A researcher finds a difference
of rejecting the between groups with a significance
