Description
Use statistical software to create, interpret, and analyze two histograms in a Word document.
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Introduction
Exploring the associations between some variables in the courseroom using correlations might provide some important information about learner success. You’ll need to pay attention to both magnitude, which is the strength of the association, and directionality, which is the direction (positive or negative) of the association. During this assessment, you’ll start learning about how to best approach correlational analyses like these and start getting some answers. You’ll explore the relationships that may or may not exist in your courseroom data.
In this assessment, you’ll get a chance to run and interpret your first inferential statistics analysis: correlations. Your readings and the Course Study Guide will help you in your efforts.
Instructions
For this assessment, you will use the Data Analysis and Application template (DAA Template [DOCX] Download DAA Template [DOCX]).
For help with statistical software, refer to the JASP Step-by-Step: Correlations [PDF] Download JASP Step-by-Step: Correlations [PDF]document.
View JASP Speedrun: Correlations [Video] for a brief tutorial video on this assessment.
Refer to the 7864 Course Study Guide [PDF] Download 7864 Course Study Guide [PDF]for information on analyses and interpretation.
For information on the data set, refer to the 7864 Data Set Instructions [PDF] Download 7864 Data Set Instructions [PDF]document.
The grades.jasp Download grades.jaspfile is a sample data set. The data represent a teacher’s recording of student demographics and performance on quizzes and a final exam across three sections of the course.
This assessment is on correlations. You will analyze the following variables in the grades.jasp Download grades.jaspdata set:
Variables and Definitions
Variable Definition
Quiz 1 Quiz 1: number of correct answers
GPA Previous grade point average
Total Total number of points earned in class
Final Final exam: number of correct answers
The DAA Template [DOCX] Download DAA Template [DOCX]has five sections:
Data Analysis Plan.
Testing Assumptions.
Results & Interpretation.
Statistical Conclusions.
Application.
Step 1: Write Section 1 of the DAA: Data Analysis Plan
Name the four variables used in this analysis and whether they are categorical or continuous.
State a research question, null hypothesis, and alternate hypothesis for the total-final correlation.
State a research question, null hypothesis, and alternate hypothesis for the gpa-quiz1 correlation.
Step 2: Write Section 2 of the DAA: Testing Assumptions
Test for one of the assumptions of correlation—normality.
Create a descriptive statistics table in the statistical software to assess normality. This table should include the four variables named above including skew and kurtosis for each variable.
Paste the table in the DAA template.
Interpret the skewness and kurtosis values and determine whether the assumption of normality was violated or not violated.
Step 3: Write Section 3 of the DAA: Results & Interpretation
Using the statistical software, paste the intercorrelation matrix for the four variables into the document.
Below the output, first report the total-final correlation including degrees of freedom, correlation coefficient, and p value. Specify whether or not to reject the null hypothesis for this correlation.
Second, report the gpa-quiz1 correlation including degrees of freedom, correlation coefficient, and p value. Specify whether or not to reject the null hypothesis for this correlation.
Step 4: Write Section 4 of the DAA: Statistical Conclusions
Provide a brief summary of your analysis and the conclusions drawn about correlations.
Analyze the limitations of the statistical test and/or possible alternative explanations for your results.
Step 5: Write Section 5 of the DAA: Application
Analyze how you might use correlations in your field of study.
Name two variables that would work for such an analysis and why studying the relationship may be important to the field or practice.
Submit your completed DAA Template as an attached Word document in the assessment area.
Software
The following statistical analysis software is required to complete your assessments in this course:
Jeffreys’s Amazing Statistics Program (JASP).
Refer to the Tools and Software: JASP page on Campus for general information. Make sure that your statistical software is downloaded, installed, and running properly on your computer.
Competencies Measured
By successfully completing this assessment, you will demonstrate your proficiency in the course competencies through the following assessment scoring guide criteria:
Competency 1: Analyze the computation, application, strengths, and limitations of various statistical tests.
Analyze statistical assumptions.
Competency 2: Analyze the decision making process of data analysis.
Articulate the data analysis plan.
Competency 3: Apply knowledge of hypothesis testing.
Interpret statistical results and hypotheses.
Competency 4: Interpret the results of statistical analyses.
Explain statistical conclusions, the limitations of the test, and/or possible alternative explanations.
Competency 6: Apply the results of statistical analyses (your own or others) to your field of interest or career.
Analyze the potential applications of the test in the field and their implications.
Competency 7: Communicate in a manner that is scholarly, professional, and consistent with the expectations for members in the identified field of study.
Communicate in a manner that is scholarly and professional, and adheres to APA style and formatting.
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7864 Data Set Instructions
The 7864 data set is fictional data. The data represents a teacher’s recording of student
demographics and academic performance across three sections of their course. Each course
section consists of about 35 students (N = 105).
The data set is located on grades.jasp. You can download grades.jasp from the 7864
assignments instructions area. It will then open in JASP.
There are 21 variables in the course data set. Refer to the table below.
Values
Scale of
measurement
JASP variable
Definition
id
Student identification number
Nominal
lastname
Student last name
Nominal
firstname
Student first name
Nominal
genderidentity
Student gender identity
1 = woman; 2 = man; 3 =
transgender; 4 = nonbinary/non-conforming; 5 =
prefer not to disclose
ethnicity
Student ethnicity
1 = Native American; 2 = Asian;
3 = Black; 4 = White; 5 =
Hispanic
Nominal
year
Class rank
1 = freshman; 2 = sophomore;
3 = junior; 4 = senior
Ordinal
lowup
Lower or upper division
1 = lower; 2 = upper
Nominal
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
Quiz 2: number of correct answers
Scale
quiz3
Quiz 3: number of correct answers
Scale
quiz4
Quiz 4: number of correct answers
Scale
Nominal
1
Values
Scale of
measurement
JASP variable
Definition
quiz5
Quiz 5: number of correct answers
Scale
final
Final exam: number of correct
answers
Scale
total
Total number of points earned
Scale
percent
Final percent
Scale
grade
Final letter grade (A, B, C, D, F)
Nominal
passfail
Passed or failed the course? 1 =
pass; 0 = fail
Nominal
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7864 Course Study Guide
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Table of Contents
Table of Contents
Week 1: Basics of Data Collection and Analysis
Scales of Measurement
Hypothesis Testing
Null and Alternative Hypotheses
Type I and Type II Errors
Probability Values and the Null Hypothesis
Preview of APA Skills
Week 2: Exploring Statistical Software and Descriptive Statistics
Screening Data
Measures of Central Tendency and Dispersion
Skewness and Kurtosis
Outliers
APA Focus of the Week: Ethics
Week 3: Correlation Introduction
Statistics and Ethics
Interpreting Correlation
Assumptions of Correlation
Hypothesis Testing of Correlation
Alternative Correlation Coefficients
APA Focus of the Week: Format Requirements
Week 4: Correlation Application
Proper Reporting of Correlations
r, Degrees of Freedom, and Correlation Coefficient
Probability Values
APA Focus of the Week: Reporting Standards in APA Format
Week 5: t-Test Introduction
Logic of the t-test
Assumptions of the t-test
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Hypothesis Testing for a t-test
APA Focus of the Week: Scholarly Writing
Week 6 – t-Test Application
Testing Assumptions: The Levene Test
Proper Reporting of the Independent Samples t-test
t, Degrees of Freedom, and t Value
Probability Value
APA Focus of the Week: Grammar and Usage – Verb Tense
Week 7: One-Way ANOVA Introduction
Advantage of ANOVA
Logic of a “One-Way” ANOVA
Avoiding Inflated Type I Error
Hypothesis Testing in a One-Way ANOVA
Assumptions of a One-Way ANOVA
APA Focus of the Week: Bias-free Language
Week 8: ANOVA Application
Proper Reporting of the One-Way ANOVA
F, Degrees of Freedom, and F Value
Probability Value
Post-Hoc Tests
APA Focus of the Week: In-text Citations
Week 9: Regression Introduction
Logic of a Simple Linear Regression
Hypothesis Testing in Simple Linear Regression
Assumptions of a Simple Linear Regression
APA Focus of the Week: References
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Week 1: Basics of Data Collection and Analysis
This study guide is designed to highlight important information and help clarify
difficult concepts. Use it as you work through your readings and assignments.
Scales of Measurement
Quantitative researchers collect data and assign numbers to their observations.
An important concept in understanding variables is the scales of measurement. There
are four scales of measurement—nominal, ordinal, interval, and ratio. These four
scales of measurement are routinely reviewed in introductory statistics textbooks as
the classic way of differentiating measurements. However, the boundaries between the
measurement scales are fuzzy. For example, is intelligence quotient (IQ) measured on
the ordinal or interval scale? In 7864, we rely on a simple measurement dichotomy:
categorical (qualitative) variables and continuous (quantitative) variables.
A categorical variable measures things that belong to a group (a category).
Nominal variables have two or more categories that are not assigned in any particular
order. For example, a nominal variable of “fruit” could assign an arbitrary number for
each category, such as apple = 1, banana = 2, and grape = 3. Ordinal variables
consist of categories with a particular order such as first place, second place, and third
place in a contest. In the 7864 data set, categorical variables like “review” are useful in
comparing students who did not complete a review session (1 = no) to those who did
complete a review session (2 = yes).
A continuous variable represents a difference in the magnitude of something
along a continuum, such as a measurement of “low to high” statistics anxiety. Interval
variables have equal points on a scale such as a Celsius scale. A ratio variable has
an additional property beyond equal intervals–a “true zero.” An example is the Kelvin
scale, and the true zero is the complete absence of heat.
In the 7864 data set, an example of a continuous variable is “quiz1,” which is a
student’s number of correct answers on the first quiz. It is important to distinguish
between categorical variables and continuous variables in 7864. In many statistical
software programs, for example, categorical variables are labeled as “Nominal” or
“Ordinal,” and interval variables and ratio variables are labeled as “Scale.” Knowing how
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to differentiate variables according to the scale of measurement will help you choose
the correct statistical test for a given hypothesis.
Hypothesis Testing
A hypothesis is an educated guess of what the researcher will observe once the
data are gathered. Probability is crucial for hypothesis testing. In hypothesis testing, you
want to know the likelihood that your results occurred by chance. No matter how
unlikely, there is always the possibility that your results have occurred by chance, even
if that probability is less than 1 in 20 (5%). However, you are likely to feel more confident
in your inferences if the probability that your results occurred by chance is less than 5%
compared to, say, 50%.
In high-stakes research (such as testing a new cancer drug), researchers may
want to be even more conservative in designating an alpha level, such as less than 1 in
100 (1%) that the results are due to chance. However, most researchers in the social
sciences find it reasonable to designate less than a 5% chance as a cutoff point for
determining statistical significance. This cutoff point is referred to as the alpha level or p
value (p < .05). An alpha level is set to determine when a researcher will reject or fail to
reject a null hypothesis (discussed next). The alpha level is set before data are
analyzed to avoid "fishing" for statistical significance.
Null and Alternative Hypotheses
When comparing groups, the null hypothesis (H0) predicts that group means
will not differ. When testing the strength of a relationship between two variables, the
null hypothesis is no relationship between variable X and variable Y. By contrast, the
alternative hypothesis (H1) does predict a difference between the two groups, or in
the case of relationships, that two variables are significantly related. An alternative
hypothesis can be directional (H1: Group X has a higher mean score than Group Y) or
nondirectional (H1: Group X and Group Y will differ).
In hypothesis testing, you either reject or fail to reject the null hypothesis.
Failing to reject the null hypothesis is not stating that you accept the null hypothesis
as true. You have simply failed to find statistical justification to reject the alternative
hypothesis.
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Type I and Type II Errors
If you commit a Type I error, this means that you have incorrectly rejected a
true null hypothesis. You have incorrectly concluded that there is a significant
difference between groups, or a significant relationship, where no such difference or
relationship actually exists. Type I errors have real-world significance, such as
concluding that an expensive new cancer drug works when actually it does not work,
costing money and potentially endangering lives. Keep in mind that you will probably
never know whether the null hypothesis is "true" or not, as we can only determine that
our data fail to reject it.
Reject H0
Do Not Reject H0
H0 is True
Type I error
Correct
H0 is False
Correct
Type II error
If you commit a Type II error, this means that you have not rejected a false
null hypothesis when you should have rejected it. You have incorrectly concluded
that no differences or no relationships exist when they actually do exist. Type II
errors also have real-world significance, such as concluding that a new cancer drug
does not work when it actually does work and could save lives.
Your alpha level (p-value) will affect the likelihood of making a Type I or a Type II
error. If your alpha level is small (such as .01, less than 1 in 100 chance), you are less
likely to reject the null hypothesis, so you are less likely to commit a Type I error.
However, you are more likely to commit a Type II error.
Probability Values and the Null Hypothesis
The statistic used to determine whether or not to reject a null hypothesis is
referred to as the calculated probability value or p value, denoted p. When you run
an inferential statistic in statistical software, it will provide you with a p value for that
statistic. If the test statistic has a probability value of less than 1 in 20 (.05), we can
say "p
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