Description
INTRODUCTION: You’re starting to learn some important information about your data, but you still want to know more. It’s time for a one-way analysis of variance (ANOVA). Unlike t-tests, which only allow for comparisons of two groups, ANOVA will allow you to examine potential group differences for variables with multiple levels.
INSTRUCTIONS: For this assessment:
Use the Data Analysis and Application template (DAA Template [DOCX] Download DAA Template [DOCX]).
For help with the statistical software, refer to the JASP Step-by-Step: ANOVA [PDF] Download JASP Step-by-Step: ANOVA [PDF]document.
View JASP Speedrun: ANOVA [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 ANOVA. You will analyze the following variables in the grades.jasp Download grades.jaspdata set:
Variables and Definitions
Variable Definition
Section Class section
Quiz3 Quiz 3: number of correct answers
Step 1: Write Section 1 of the DAA: Data Analysis Plan
Name the variables used in this analysis and whether they are categorical or continuous.
State a research question, null hypothesis, and alternate hypothesis for the ANOVA.
Step 2: Write Section 2 of the DAA: Testing Assumptions
Test for one of the assumptions of ANOVA – homogeneity.
Create statistical software output showing the Levene’s Test for Equality of Variances.
Paste the table in the DAA template.
Interpret the homogeneity test to determine whether the assumption of homogeneity is violated or is not violated.
Step 3: Write Section 3 of the DAA: Results & Interpretation
If the homogeneity assumption is not violated (Section 2), run the “Homogeneity corrections: None” version of the ANOVA. Follow up with the “Standard” version of the Tukey post hoc test.
However, if the homogeneity assumption is violated (Section 2), run the “Homogeneity corrections: Welch” version of the ANOVA. Follow up with the “Games-Howell” version of the Tukey post hoc test.
Paste the following statistical software tables into the document:
Descriptives table.
ANOVA table.
Post Hoc Tests table (Tukey correction).
Below the output:
Report the means and standard deviations of quiz3 for each group of the section variable.
Report the results of the F test and interpret the statistical results against the null hypothesis; state whether the null hypothesis is rejected or not rejected.
Finally, if the F is significant, interpret the post-hoc tests.
Step 4: Write Section 4 of the DAA: Statistical Conclusions
Provide a brief summary of your analysis and the conclusions drawn about this ANOVA.
Analyze the limitations of the statistical test and/or possible alternative explanations for your results.
Step 5: Write Section 5 of the DAA: Application
Name an independent variable (the IV should have three or more groups or categories) and dependent variable that would work for such an analysis and why studying it may be important to the field or practice.
Submit your 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.
Unformatted Attachment Preview
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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