Prepared by Sarah Perry Johnson
Review of Levels of Measurement
 The 4 Levels of Measurement are:
 Nominal
 Ordinal
 Interval
 Ratio
 The subsequent slides will allow us to revisit each level
of measurement and review the characteristics of each
variable.
Nominal Variable
 Nominal (nom=name)
 Qualitative
 No numerical value
 Discreet
 Examples: religion, nationality, occupation, etc.
 Nominal variables are also considered to be
categorical.
Ordinal Variables
Ordinal (order)
 Quantitative
 In order of cases greater than or less than; a range
 Discreet
 Examples: level of conflict (low to high), socioeconomic
status (SES), Starbucks sizes, educational attainment,
etc.
Interval Variables
Interval
 Quantitative
 Numerical/integer value; no absolute/fixed “0” point
 Continuous
 Example: temperature, depression score (starts at 6,
ends at 60)
Ratio Variables
Ratio
 Quantitative
 Numerical/integer value; has an absolute fixed “zero”
point
 Continuous
 Examples: number of children, number of cigarettes
smoked, number of feet/miles, number of votes
Basic Template for
Relationships Questions
 Relationships question:
Is there a relationship between [the IV] and [the
DV]?
 Example: Is there a relationship between the number
of hours a person studies per day and GPA?
 Independent Variable: # of daily study hours
 Dependent Variable: Grade Point Average (GPA)
 Used for Pearson, Spearman, and Regression
Questions
Basic Template for
Differences Questions
 Differences question:
Is there a difference between [categories of the IV]
based on [the DV]?
 Is there a difference between the United States, China,
and Sweden based on GDP?
 Independent Variable: countries (US, China, and
Sweden)
 Dependent Variable: Gross Domestic Product (GDP
score)
 Used for Chi-Square, T-Test, and ANOVA Questions
Charts and Templates
Six types of Tests:
Variables needed
Test Name
IV
DV
Symbol
Chi-Square
Discreet
Discreet
χ²
T-Test
Discreet
Continuous
t
ANOVA
Discreet (2+)
Continuous
F
Pearson
Correlation
Continuous
Continuous
r
Spearman
Correlation
Ordinal
Ordinal
rs
Regression
Continuous
Continuous
--
Chi-Square Test:
Variables and Reporting
Chi-Square Test
 Independent Variable: Discreet
 Dependent Variable: Discreet
Report template
 Is there is a difference between [categories of the IV]
based on the [DV]?
 There is a difference between [categories of the IV]
based on the [DV] (chi-square[χ²=?], p-value[p=?]).
t-Test:
Variables and Reporting
t-Test
 Independent Variable: Discreet (limit: 2 categories)
 Dependent Variable: Continuous
Report template
 Is there is a difference between [categories of the IV]
based on the [DV]?
 There is a difference between [categories of the IV]
based on the [DV] (t-score[t=?], p-value[p=?]).
 State which category of the IV has more...[Cat 1 has
around __% more than Cat 2.]
ANOVA:
Variables and Reporting
ANOVA
 Independent Variable: Discreet (2 or more categories)
 Dependent Variable: Continuous
Report Template
 Is there is a difference between [2+ categories of the IV] based on the
[DV]?
 There is a difference between [2+ categories of the IV] based on the
[DV] (F-score[F=?], p-value[p=?]).
 State which category of the IV has the most and the least [Cat 1 has the
most and Cat 2 has the least. There is no significant difference between
Cat 3, however, the difference between Cat 1 and Cat 2 were
significant.]
Pearson Correlation:
Variables and Reporting
Pearson Correlation
 Independent Variable: Continuous
 Dependent Variable: Continuous
Report Template
 Is there is a relationship between [the IV] and [the DV]?
 There is a relationship between [the IV] and [the DV] (r-score[r=?], pvalue [p=?]).
 State the strength and direction: This is a [state strength], [state
direction] relationship.
 State the R² (square the r value): [The IV] explains about __% of the
variance in [the DV].
Spearman Correlation:
Variables and Reporting
Spearman Correlation
 Independent Variable: Ordinal
 Dependent Variable: Ordinal
Report Template
 Is there a relationship between [the IV] and [the DV]?
 There is a relationship between [the IV] and [the DV] (rsscore[ rs=?], p-value [p=?]).
 State the strength and direction: This is a [state strength],
[state direction] relationship.
 No R-square: ordinal variables
Regression:
Variables and Reporting
Regression
 Independent Variable: Continuous
 Dependent Variable: Continuous
Regression:
Variables and Reporting (cont.)
 Is there a relationship between [the IV] and [the DV]?
 There is a relationship between [the IV] and [the DV]
(p-value[p=?]).
 State the strength and direction: This is a [state
strength], [state direction] relationship.
Regression:
Variables and Reporting (cont.)
 State the slope: For each additional [1 unit of the IV] of the
[units of analysis], the [DV] is expected to
[increase/decrease] by [# units of the DV].
 State the R² (square the r value): [The IV] explains about
__% of the variance in [the DV].
 State the y-intercept: In the case that [the IV] is 0, it is
predicted that [the DV] will be [amount and units of
measurement].
 Or: A [unit of analysis] that is [units of measurement of
IV] is predicted to be [amount and units of measurement
of DV]
Multiple Regression:
Variables and Reporting
Multiple Regression
 Independent Variable: Continuous (2+)
 Dependent Variable: Continuous
Report Template:
 Is there a relationship between [IV#1], [IV#2], and
[IV#3] with [the DV]?
 State the Adjusted R2: [IV#1], [IV#2], and [IV#3]
together explain about [___%] of the variance in [the
DV].
Multiple Regression:
Variables and Reporting (cont.)
 Report on the Adjusted R²: [IV#1, IV#2, and IV#3]
together explain about __% of the variance in [the
DV].
 Next, state the slope for each IV with the DV.
 Hint: if you have three IV’s, you should write three
separate statements: IV#1/DV, IV#2/DV, and IV#3/DV.
(see next slide…)
Multiple Regression:
Variables and Reporting (cont.)
 For each additional [1 unit of the IV#1] of the [units of
analysis], the [DV] is expected to [increase/decrease] by [#
units of the DV], holding constant for [IV#2] and [IV#3]
(p=).
 For each additional [1 unit of the IV#2] of the [units of
analysis], the [DV] is expected to [increase/decrease] by [#
units of the DV], holding constant for [IV#1] and [IV#3]
(p=).
 For each additional [1 unit of the IV#3] of the [units of
analysis], the [DV] is expected to [increase/decrease] by [#
units of the DV], holding constant for [IV#1] and [IV#2]
(p=).
Multiple Regression:
Variables and Reporting (cont.)
 Each time you report on a slope, add to the end of the
statement “holding constant for” and list the leftover
variables.
 For example: For each additional [1 unit of the IV#1] of the
[units of analysis], the [DV] is expected to
[increase/decrease] by [# units of the DV], holding
constant for [IV#2 and IV#3] (p=).
 For the test, regarding the slope, you will only have to
report on one of the IV’s paired with the DV.
Strength and Direction of
Relationship between Variables
r -Value
<0.20
Strength of Relationship
Slight or weak, almost negligible
relationship
R²
<0.04
o.20-o.40
Low correlation, definite but very small
relationship
0.04-0.16
0.40-0.70
Moderate correlation, substantial
relationship
0.16-0.49
0.70-0.90
High or strong correlation, marked
relationship
0.49-0.81
>0.90
Very high correlation, very dependable
relationship
>0.81
Example: Pearson correlationStrength and Direction
Is there a relationship between self-concept scores and depression
scores? To determine whether there is a statistically significant
relationship between the variables, look at the p-value. To determine
the strength and direction of the relationship, look at the r-value.
Strength and Direction
(continued)
Strength of the relationship
 According to our chart, the integer value 0.852 shows
that there is a very high/strong relationship between
self-concept scores and depression scores.
Direction of the relationship
 According to our chart, the negative sign (-) in front of
the integer denotes that the relationship is a negative
one (as X increases, Y decreases).
So how shall we report this data for a
Pearson’s Correlation?
Strength and Direction
(continued)
Report template for Pearson’s correlation
 Is there is a relationship between [the IV] and [the DV]?
 There is a difference between [the IV] and [the DV] (r-
score[r=?], p-value [p=?]).
 State the strength and direction: This is a [state strength],
[state direction] relationship.
Report:
 There is a relationship between self-concept scores and
depression scores (r=-0.852; p=0.004).
 This is a very strong, negative relationship.
Example: Spearman’s Rho
Correlations
Year in
college
Spearm an's rho
Year in college
Correlation Coefficient
Sig. (2-tailed)
N
General Happiness
General
Happiness
1.000
.290*
.
.027
58
58
Correlation Coefficient
.290*
Sig. (2-tailed)
.027
.
58
58
N
*. Correlation is s ignificant at the 0.05 level (2-tailed).
According to the above Spearman’s rho chart, rs =0.290.
Direction:
The integer value is positive/negative.
Therefore, the direction of the relationship is positive/negative.
Strength:
According to the strength chart, the value is____________.
Therefore, the strength of the relationship is ____________.
1.000
Spearman’s Rho
(continued)
 Time to report on the value for a Spearman’s rho:
 There is a relationship between __________ and
__________ (rs=_____;p=_____). This is a
________________ relationship.
Most and Least
 Report on the most and least based on the means
report.
Variable to Quantify: Jelly beans
 Sue: 56
 Jenny: 39
 Carly: 45
 Sue has the most jelly beans and Jenny has the least
[amount of jelly beans].
Most and Least
(continued)
Let’s evaluate the same type of example from Lab 8.
Report
AGE OF RESPONDENT
VOTE FOR CLINTON,
BUSH, PEROT
Bush
Mean
N
Std. Deviatio n
48.64
661
16.742
Perot
41.50
278
12.612
Clinton
49.34
908
16.597
Total
47.91
1847
16.334
What is the unit of measurement? (Hint-it is contained in the box above
the table…)
What is the largest value?
What is the smallest value?
Most and Least
(continued)
Variable to quantify: age
Descriptors for least and most in relationship to age
 Least=Youngest
 Most=Oldest
 Perot voters are the youngest and the Clinton voters
are the oldest.
-Or People who voted for Perot are the youngest and
people who vote for Clinton are the oldest.