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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