Assessment 2 ContextIn many data analyses, it is desirable.docx

Assessment 2 Context
In many data analyses, it is desirable to compute a coefficient
of association. Coefficients of association are quantitative
measures of the amount of relationship between two variables.
Ultimately, most techniques can be reduced to a coefficient of
association and expressed as the amount of relationship between
the variables in the analysis. There are many types of
coefficients of association. They express the mathematical
association in different ways, usually based on assumptions
about the data. The most common coefficient of association you
will encounter is the Pearson product-moment correlation
coefficient (symbolized as the italicized r), and it is the only
coefficient of association that can safely be referred to as
simply the "correlation coefficient". It is common enough so
that if no other information is provided, it is reasonable to
assume that is what is meant.
Correlation coefficients are numbers that give information about
the strength of relationship between two variables, such as two
different test scores from a sample of participants. The
coefficient ranges from -1 through +1. Coefficients between 0
and +1 indicate a positive relationship between the two scores,
such as high scores on one test tending to come from people
with high scores on the second. The other possible relationship,
which is every bit as useful, is a negative correlation between -1
and 0. A negative correlation possesses no less predictive power
between the two scores. The difference is that high scores on
one measure are associated with low scores on the other.
An example of the kinds of measures that might correlate
negatively is absences and grades. People with higher absences

will be expected to have lower grades. When a correlation is
said to be significant, it can be shown that the correlation is
significantly different form zero in the population. A correlation
of zero means no relationship between variables. A correlation
other than zero means the variables are related. As the
coefficient gets further from zero (toward +1 or -1), the
relationship becomes stronger.Interpreting Correlation:
Magnitude and Sign
Interpreting a Pearson's correlation coefficient (rXY) requires
an understanding of two concepts:
· Magnitude.
· Sign (+/-).
The magnitude refers to the strength of the linear relationship
between Variable X and Variable
The rXY ranges in values from -1.00 to +1.00. To determine
magnitude, ignore the sign of the correlation, and the absolute
value of rXY indicates the extent to which Variable X and
Variable Y are linearly related. For correlations close to 0, there
is no linear relationship. As the correlation approaches either -
1.00 or +1.00, the magnitude of the correlation increases.
Therefore, for example, the magnitude of r = -.65 is greater than
the magnitude of r = +.25 (|.65| > |.25|).
In contrast to magnitude, the sign of a non-zero correlation is
either negative or positive.
These labels are not interpreted as "bad" or "good." Instead, the
sign represents the slope of the linear relationship between X
and Y. A scatter plot is used to visualize the slope of this linear
relationship, and it is a two-dimensional graph with dots
representing the combined X, Y score. Interpreting scatter plots
is necessary to check assumptions of correlation discussed
below.
A positive correlation indicates that, as values of X increase,

the values of Y also increase (for example, grip strength and
arm strength). You may wish to view examples of positive and
negative correlations as viewed by a scatter plot.
Assumptions of Correlation
All inferential statistics, including correlation, operate under
assumptions that are checked prior to calculating them in SPSS.
Violations of assumptions can lead to erroneous inferences
regarding a null hypothesis. The first assumption is
independence of observations for X and Y scores. The
measurement of individual X and Y scores should not be
influenced by errors in measurement or problems in research
design (for example, a student completing an IQ test should not
be looking over the shoulder of another student taking that test;
his or her IQ score should be independent). This assumption is
not statistical in nature; it is controlled by using reliable and
valid instruments and by maintaining proper research
procedures to maintain independence of observations.
The second assumption is that, for Pearson's r, X and Y are
quantitative, and that each variable is normally distributed.
Other correlations discussed below do not require this
assumption, but Pearson's r is the most widely used and reported
type of correlation. It is therefore important to check this
assumption when calculating Pearson's r in SPSS. This
assumption is checked by a visual inspection of X and Y
histograms and calculations of skew and kurtosis values.
The third assumption of correlation is that X, Y scores are
linearly related. Correlation does not detect strong curvilinear
relationships. This assumption is checked by a visual inspection
of the X, Y scatter plot.
The fourth assumption of correlation is that the X, Y scores
should not have extreme bivariate outliers that influence the
magnitude of the correlation. Bivariate outliers are also detected
by a visual examination of a scatter plot. Outliers can

dramatically influence the magnitude of the correlation, which
sometimes leads to errors in null hypothesis testing. Bivariate
outliers are particularly problematic when a sample size is small
and suggests an N of at least 100 for studies that report
correlations.
The fifth assumption of correlation is that the variability in Y
scores is uniform across levels of X. This requirement is
referred to as the homogeneity of variance assumption, which is
usually difficult to assess in scatter plots with a small sample
size. This assumption is typically emphasized when checking
the homogeneity of variance for a t-test or analysis of variance
(ANOVA) studied later in the course.
Hypothesis Testing of Correlation
The null hypothesis for correlation predicts no significant linear
relationship between X and Y, or H0: rXY = 0. A directional
alternative hypothesis for correlation is either an expected
significant positive relationship (H1: rXY > 0) or significant
negative relationship (H1: rXY < 0). A non-directional
alternative hypothesis would simply predict that the correlation
is significantly different from 0, but it does not stipulate the
sign of the relationship (H1: rXY ≠ 0). For correlation as well
as t-tests and ANOVA studied later in the course, the standard
alpha level for rejecting the null hypothesis is set to .05. SPSS
output for a correlation showing a p value of less than .05
indicates that the null hypothesis should be rejected; there is a
significant relationship between X and Y. A p value greater than
.05 indicates that the null hypothesis should not be rejected;
there is not a significant relationship between X and Y.Effect
Size in Correlation
Even if the null hypothesis is rejected, how large is the
association between X and Y? To provide additional context,
the interpretation of all inferential statistics, including
correlation, should include an estimate of effect size. An effect

size is articulated along a continuum from "small," to
"medium," to "large."
An effect size for correlation is an estimate of the strength of
association between X and Y in unit-free terms (that is, effect
size estimation is independent of how X and Y are originally
measured). Another advantage is that an effect size is calculated
independently from the sample size of the study, as any non-
zero correlation will be significant if the sample size is large
enough. The effect size for correlation is calculated as r2
(pronounced "r-square"), and it is simply the squared value of r.
For example, r = .50 results in an effect size r2 = .25 (.52 =
.25).
Roughly speaking, a correlation less than or equal to .10 is
"small," a correlation between .10 and .25 is "medium," and a
correlation above .25 is "large" (Warner, 2013).Alternative
Correlation Coefficients
The most widely used correlation is referred to as Pearson's r.
Pearson's r is calculated between X and Y variables that are
measured on either the interval or ratio scale of measurement
(for example, height and weight). There are other types of
correlation that depend on other scales of measurement for X
and Y. A point biserial (rpb) correlation is calculated when one
variable is dichotomous (for example, gender) and the other
variable is interval/ratio data (for example, weight). If both
variables are ranked (ordinal) data, the correlation is referred to
as Spearman's r (rs). Although the underlying scales of
measurement differ from the standard Pearson's r, rpb and rs
values are both calculated between -1.00 and +1.00 and are
interpreted similarly.
If both variables are dichotomous, the correlation is referred to
as phi (ɸ). A final test of association is referred to as chi-
square. Phi and chi-square are studied in Advanced Inferential

Statistics.
Correlation – Application
We will apply our understanding of correlation in the third IBM
SPSS assessment. For the remaining data analysis assessments
in this course, we will use the Data Analysis and Application
(DAA) template. The DAA is separated into five
sections:Section 1: Data File Description
· Describe the context of the data set.
· Specify the variables used and their scale of measurement.
· Specify sample size (N).Section 2: Testing Assumptions
· Articulate the assumptions of a statistical test.
· Provide SPSS output that tests assumptions and interpret
them.Section 3: Research Question, Hypotheses, and Alpha
Level
· Articulate a research question relevant to the statistical test.
· Articulate the null hypothesis and alternative hypothesis.
· Specify the alpha level.Section 4: Interpretation
· Provide SPSS output for an inferential statistic and report it.
· Interpret statistical results against the null hypothesis.
· State conclusions.
· Analyze strengths and limitations of the statistical test.
Section 5: Conclusions
· State conclusions.

· Analyze strengths and limitations of the statistical test.Proper
Reporting of Correlations
Reporting a correlation in proper APA style requires an
understanding of the following elements, including the
statistical notation for a Pearson's correlation ( r ), the degrees
of freedom, the correlation coefficient, the probability value,
and the effect size. Consider the following example:
Only the correlation between organizational commitment (OC)
and organizational citizenship behavior (OCB) was statistically
significant, r(110) = +.22, p < .05 (two-tailed). The r2 was .05;
thus, only about 5% of the variance in OC scores could be
predicted from OCB scores; this is a weak positive
relationship.r, Degrees of Freedom, and Correlation Coefficient
The statistical notation for Pearson's correlation is r, and
following it is the degrees of freedom for this statistical test
(for example, 110). The degrees of freedom for Pearson's r is N
– 2, so there were 112 participants in the sample cited above
(112 – 2 = 110). Note that SPSS output for Pearson's r provides
N, so you must subtract 2 from N to correctly report degrees of
freedom. Next is the actual correlation coefficient including the
sign. After the correlation coefficient is the probability
value.Probability Values
Prior to the widespread use of SPSS and other statistical
software programs, p values were often calculated by hand. The
convention in reporting p values was to simply state, "p < .05"
to reject the null hypothesis and "p > .05" to not reject the null
hypothesis. However, SPSS provides an "exact" probability
value, so it should be reported instead.
Hypothetical examples would be "p = .02" to reject the null
hypothesis and "p = .54" to not reject the null hypothesis (round
exact p values to two decimal places). One confusing point of
SPSS output is that highly significant p values are reported as
".000," because SPSS only reports probability values out to

three decimal places. Remember that there is a "1" out there
somewhere, such as p = .000001, as there is always some small
chance that the null hypothesis is true. When SPSS reports a p
value of ".000," report "p < .001" and reject the null hypothesis.
The "(two-tailed)" notation after the p value indicates that the
researcher was testing a nondirectional alternative hypothesis
(H1: rXY ≠ 0). He or she did not have any a priori justification
to test a directional hypothesis of the relationship between
commitment and length of the relationship. In terms of alpha
level, the region of rejection was therefore 2.5% on the left side
of the distribution and 2.5% on the right side of the distribution
(2.5% + 2.5% = 5%, or alpha level of .05). A "(one-tailed)"
notation indicates a directional alternative hypothesis. In this
case, all 5% of the region of rejection is established on either
the left side (negative; (H1: rXY < 0) or right side (positive;
(H1: rXY > 0) of the distribution. A directional hypothesis must
be justified prior to examining the results. In this course, we
will always specify a two-tailed (non-directional) test, which is
more conservative relative to a one-tailed test. The advantage is
that a nondirectional test detects relationships or differences on
either side of the distribution, which is recommended in
exploratory research.Effect Size
Effect sizes provide additional context for the strength of the
relationship in correlation. Effect sizes are important because
any non-zero correlation will be statistically significant if the
sample size is large enough. After the probability value is
stated, provide the r2 effect size and interpret it as small,
medium, or large. It is good form to report the effect size for
both significant and nonsignificant statistics for meta-analyses
(that is, statistical studies that combine the results across
multiple independent research studies), but in journal articles
where space is limited, authors will often just report effect sizes
for statistics that reject the null hypothesis.ReferencesLane, D.
M. (2013). HyperStat online statistics textbook. Retrieved from
http://davidmlane.com/hyperstat/index.htmlWarner, R. M.
(2013). Applied statistics: From bivariate through multivariate

techniques (2nd ed.). Thousand Oaks, CA: Sage Publications.
1
3
Scoring Guide ToolPrintPSY-FP7864 - Section 02
[u02a1] - CorrelationMoore , Ashley
Overall Comments
Great job overall! I didn't see section 1. Make sure to provide a
description of the variables including their scales of
measurement and the type of correlations that would be used for
each pair of variables. Please see my comments and let me know
if you have any questions.
LorieCriterionNon-
performanceBasicProficientDistinguishedCriterion
Apply the appropriate SPSS
procedures to check assumptions and calculate the correlations.
(14%)
Competency

Apply a statistical program's procedure to data.
not selected
Does not
provide SPSS output.
not selected
Provides

SPSS output with errors.
not selected
Applies the
appropriate SPSS procedures to check assumptions and
calculate the correlations.
selected

Distinguished
Analyzes the
SPSS procedures to check assumptions and calculate the
correlations in an exemplary manner.
Comments:
Good job using SPSS to analyze the data with correlations!
Criterion
Develop a context for the data
set, including a definition of required variables and scales of
measurement.
(14%)

Competency
Apply the results of statistical analyses (your own or others) to
your field of interest or career.
selected
Non-
performance
Does not
identify a context for the data set.

not selected
Identifies a
context for the data set.
not selected
Develops a
context for the data set, including a definition of required
variables and scales of measurement.

not selected
Analyzes the
context for the data set, demonstrating insight and
understanding of relevant data required variables and scales of
measurement.
Comments:
I don't see a discussion of the four variables used in this
assessment. What are their scales of measurement? What type
of correlation would be used to analyze each pair of variables?
Criterion
Analyze the assumptions of
correlation.
(14%)

Competency
Analyze the decision-making process of data analysis.
not selected
Does not
identify the assumptions of correlation.

not selected
Identifies,
but does not analyze, the assumptions of correlation.
selected
Proficient
Analyzes the
assumptions of correlation.

not selected
Evaluates
the assumptions of correlation.
Comments:
Good. I don't really see an interpretation of the scatterplot.
There is no significance testing for skew and kurtosis. You can
only look to see if the value falls between -1 and +1.0.Criterion
Develop a research question, null
hypothesis, alternative hypothesis, and alpha level.

(14%)
Competency
Apply knowledge of hypothesis testing.
not selected
Does not
identify a research question, null hypothesis, alternative
hypothesis, and alpha level.

not selected
Identifies a
research question, null hypothesis, alternative hypothesis, and
alpha level.
selected
Proficient

Develops a
alpha level.
not selected
Develops a
alpha level, demonstrating insight and understanding of the
relevant data.
Comments:
Good. I don't see a research question stated in the form of a
question. Criterion
Interpret the correlation output.

(14%)
Competency
Interpret the results of statistical analyses.
not selected
Does not
interpret the correlation output.

not selected
Identifies,
but does not interpret, the correlation output.
not selected
Interprets
the correlation output.

selected
Distinguished
Evaluates
the correlation output, including the effect size, and specifies if
the null hypothesis is rejected or not for the correlation.
Comments:
Great job interpreting the results of the correlations! Criterion
Develop a conclusion including
strengths and limitations of correlation.

(15%)
Competency
Analyze the computation, application, strengths, and limitations
of various statistical tests.
not selected
Does not
develop a conclusion including strengths and limitations of

correlation.
not selected
Develops a
conclusion that does not include, or that includes a partial list
of, strengths and limitations of correlation.
not selected
Develops a
conclusion including strengths and limitations of correlation.

selected
Distinguished
Analyzes the
strengths and limitations of correlational analysis,
demonstrating insight and understanding of the relevant data.
Comments:

Good job! Criterion
Communicate in a manner that is
scholarly, professional, and consistent with expectations for
members of the identified field of study.
(15%)
Competency
Communicate in a manner that is scholarly, professional, and
consistent with the expectations for members in the identified
field of study.

not selected
Does not
communicate in a manner that is scholarly, professional, and
field of study.
selected
Basic
Inconsistently communicates in a manner that is scholarly,
professional, and consistent with the expectations for members
in the identified field of study.

not selected
Communicates in a manner that is scholarly, professional,
and consistent with the expectations for members in the
identified field of study.
not selected
Communicates in a manner that is professional, scholarly,
and consistent with expectations for members of the identified
field of study. Adheres to APA guidelines, and work is
appropriate for publication.

Comments:
There are quite a few errors in writing. All sentences in all
sections need to be written in complete sentences.
Scoring Guide ToolPrintPSY-FP7864 - Section 02
[u02a1] - CorrelationMoore , Ashley
Overall Comments
Great job overall! I didn't see section 1. Make sure to provide a
description of the variables including their scales of
measurement and the type of correlations that would be used for
each pair of variables. Please see my comments and let me know
if you have any questions.
LorieCriterionNon-
performanceBasicProficientDistinguishedCriterion
Apply the appropriate SPSS
procedures to check assumptions and calculate the correlations.
(14%)

Competency
Apply a statistical program's procedure to data.
not selected
Does not
provide SPSS output.

not selected
Provides
SPSS output with errors.
not selected
Applies the
appropriate SPSS procedures to check assumptions and
calculate the correlations.

selected
Distinguished
Analyzes the
SPSS procedures to check assumptions and calculate the
correlations in an exemplary manner.
Comments:
Good job using SPSS to analyze the data with correlations!
Criterion
Develop a context for the data
set, including a definition of required variables and scales of
measurement.

(14%)
Competency
Apply the results of statistical analyses (your own or others) to
your field of interest or career.
selected
Non-
performance

Does not
identify a context for the data set.
not selected
Identifies a
context for the data set.
not selected

Develops a
context for the data set, including a definition of required
variables and scales of measurement.
not selected
Analyzes the
context for the data set, demonstrating insight and
understanding of relevant data required variables and scales of
measurement.
Comments:
I don't see a discussion of the four variables used in this
assessment. What are their scales of measurement? What type
of correlation would be used to analyze each pair of variables?

Criterion
Analyze the assumptions of
correlation.
(14%)
Competency
Analyze the decision-making process of data analysis.
not selected

Does not
identify the assumptions of correlation.
not selected
Identifies,
but does not analyze, the assumptions of correlation.
selected

Proficient
Analyzes the
assumptions of correlation.
not selected
Evaluates
the assumptions of correlation.
Comments:
Good. I don't really see an interpretation of the scatterplot.

There is no significance testing for skew and kurtosis. You can
only look to see if the value falls between -1 and +1.0.Criterion
Develop a research question, null
hypothesis, alternative hypothesis, and alpha level.
(14%)
Competency
Apply knowledge of hypothesis testing.
not selected

Does not
identify a research question, null hypothesis, alternative
hypothesis, and alpha level.
not selected
Identifies a
alpha level.

selected
Proficient
Develops a
alpha level.
not selected
Develops a
alpha level, demonstrating insight and understanding of the
relevant data.

Comments:
Good. I don't see a research question stated in the form of a
question. Criterion
Interpret the correlation output.
(14%)
Competency
Interpret the results of statistical analyses.

not selected
Does not
interpret the correlation output.
not selected
Identifies,
but does not interpret, the correlation output.
not selected

Interprets
the correlation output.
selected
Distinguished
Evaluates
the correlation output, including the effect size, and specifies if
the null hypothesis is rejected or not for the correlation.

Comments:
Great job interpreting the results of the correlations! Criterion
Develop a conclusion including
strengths and limitations of correlation.
(15%)
Competency
Analyze the computation, application, strengths, and limitations
of various statistical tests.

not selected
Does not
develop a conclusion including strengths and limitations of
correlation.
not selected
Develops a
conclusion that does not include, or that includes a partial list
of, strengths and limitations of correlation.

not selected
Develops a
conclusion including strengths and limitations of correlation.
selected
Distinguished
Analyzes the
strengths and limitations of correlational analysis,
demonstrating insight and understanding of the relevant data.

Comments:
Good job! Criterion
Communicate in a manner that is
scholarly, professional, and consistent with expectations for
members of the identified field of study.
(15%)
Competency
Communicate in a manner that is scholarly, professional, and
field of study.

not selected
Does not
communicate in a manner that is scholarly, professional, and
field of study.
selected
Basic

Inconsistently communicates in a manner that is scholarly,
professional, and consistent with the expectations for members
in the identified field of study.
not selected
Communicates in a manner that is scholarly, professional,
and consistent with the expectations for members in the
identified field of study.
not selected

Communicates in a manner that is professional, scholarly,
and consistent with expectations for members of the identified
field of study. Adheres to APA guidelines, and work is
appropriate for publication.
Comments:
There are quite a few errors in writing. All sentences in all
sections need to be written in complete sentences.
Data Set Instructions
The grades.sav file is a sample SPSS data set. The fictional data
represent a teacher’s recording of student demographics and
performance on quizzes and a final exam across three sections
of the course. Each section consists of about 35 students (N =
105).Software Installation
Make sure that IBM SPSS Statistics Standard GradPack is fully
licensed, installed on your computer, and running properly. It is
important that you have either the Standard or Premium version
of SPSS that includes the full range of statistics. Proper
software installation is required in order to complete your first
SPSS data assignment in Assessment 1.

Next, click grades.sav in the Assessment 1 Resources to
download the file to your computer.
· You will use grades.sav throughout the course.
The definition of variables in the grades.sav data set are found
in the Assessment 1 Context. Understanding these variable
definitions is necessary for interpreting SPSS output.
In Assessment 1, you will define values and scales of
measurement for all variables in your grades.sav file.
Verify the values and scales of measurement assigned in the
grades.sav file using information in the Data Set on page 2 of
this document.
Data Set
There are 21 variables in grades.sav,. Open your grades.sav file
and go to the Variable View tab. Make sure you have the
following values and scales of measurement assigned.
SPSS variable
Definition
Values
Scale of measurement
id
Student identification number
Nominal
lastname
Student last name
Nominal
firstname
Student first name
Nominal
gender
Student gender
1 = female; 2 = male
Nominal
ethnicity

Student ethnicity
1 = Native; 2 = Asian; 3 = Black;
4 = White; 5 = Hispanic
Nominal
year
Class rank
1 = freshman; 2 = sophomore;
3 = junior; 4 = senior
Scale
lowup
Lower or upper division
1 = lower; 2 = upper
Ordinal
section
Class section
Nominal
gpa
Previous grade point average
Scale
extcr
Did extra credit project?
1 = no; 2 = yes
Nominal
review
Attended review sessions?
1 = no; 2 = yes
Nominal
quiz1
Quiz 1: number of correct answers
Scale
quiz2

Scale
quiz3
Scale
quiz4
Scale
quiz5
Scale
final
Final exam: number of correct answers
Scale
total
Total number of points earned
Scale
percent
Final percent
Scale
grade
Final grade
Nominal
passfail
Passed or failed the course?
Nominal

Assessment 2 ContextIn many data analyses, it is desirable.docx

More Related Content

Similar to Assessment 2 ContextIn many data analyses, it is desirable.docx

Similar to Assessment 2 ContextIn many data analyses, it is desirable.docx (20)

More from galerussel59292

More from galerussel59292 (20)

Recently uploaded

Recently uploaded (20)

Assessment 2 ContextIn many data analyses, it is desirable.docx