Prerequisite course: EDR-8200: Scholarly Literature Review

**Course Description:**

This course offers foundational knowledge to become a critical consumer of statistical-based research literature as well as develop the necessary skillset for non-inferential quantitative analyses. The emphasis will be on understanding multivariate data, non-inferential and inferential statistical concepts, the conventions of quantitative data analysis, interpretation, and critical inferences from statistical results. Statistical computations will be completed using statistical software applications for quantitative data analysis. The course culminates in a synthesis project to demonstrate statistical skills and aligned with APA guidelines for presentation of statistical results.

**Learning Outcomes:**

- Examine basic statistical concepts used in educational research.
- Analyze differences among various non-inferential and inferential statistical multivariate analyses.
- Select appropriate statistical analyses for research proposals.
- Interpret statistical results to draw inferences.
- Develop aligned research proposals appropriate for inferential hypothesis testing.

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**Course Concepts:**

- Population, Sample, and Parameters
- Types of Variables
- Levels of Measurement
- Parametric Statistical Procedures and Their Assumptions
- Nonparametric Statistical Procedures
- Selection of Appropriate Statistical Analyses
- Interpretation of Statistical Analyses and Dissemination of Results
- Formulation of Conclusions Based on Statistical Results

**Course Overview:**

**Section 1: Introduction to Statistical Concepts**

**Week 1: Basic Concepts in Statistics and Basic SPSS Functions**

##### Week 1 Assignment 1: Examine the Basic Principles and Concepts Related to Inferential Statistics (5 Points)

##### Week 1 Assignment 2: Examine the Basic Layout and Functions of SPSS (5 Points)

**Week 2: Exploring and Presenting Categorical and Continuous Data**

##### Week 2 Assignment: Develop Graphs and Frequency Distributions for Categorical and Continuous Variables (10 Points)

**Week 3: Central Tendency**

##### Week 3 Assignment: Analyze Central Tendency and Variability (10 Points)

**Section 2: Foundations of Inferential Statistics**

**Week 4: The Normal Curve and Standard Scores**

##### Week 4 Assignment: Examine the Normal Curve and Calculate Standard Scores (10 Points)

**Week 5: Issues in Inferential Statistics**

##### Week 5 Assignment: Determine the Standard Error of the Mean, Confidence Intervals, and Parametric Assumptions (10 Points)

**Section 3: Calculating Parametric and Non-Parametric Statistics**

**Week 6: Relationships Between Variables—Correlation, Regression, and Non-Parametric (Chi-Square) Procedures**

##### Week 6 Assignment: Explore Relationships Between Variables Using Correlation, Regression, And Chi-Square

**Week 7: Differences Between Groups’ t – test and Analysis of Variance, One & Two-Way (ANOVA)**

##### Week 7 Assignment: Analyze Differences Between Groups Using Paired and Independent Samples *t* – test and ANOVA (15 Points)

**Week 8: Statistical Analysis Design**

##### Week 8 Assignment: Develop a Statistical Analysis Plan (20 Points)

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Week 1 – Assignment 1: Examine the Basic Principles and Concepts Related to Inferential Statistics

Please answer each of the following questions using information from the readings.

- Population and sample:
- What is a population?
- What is a sample?

- What is the difference between a statistic and a parameter?
- What is the margin of error in statistics, and why is it important?
- What is the difference between quantitative and qualitative data?
- Describe the four levels of measurements
- Nominal
- Ordinal
- Interval
- Ratio

- Provide examples of variables found in educational research that exist in each of the four levels of measurement described above.
- Nominal
- Ordinal
- Interval
- Ratio

- What is a hypothesis?
- What is a hypothesis test?
- Statistical hypothesis:
- What is the null hypothesis?
- What is the alternative hypothesis?

- Please explain what a p-value is for a hypothesis test.

Length: Complete responses to all parts of all 10 questions. Please include the question prompts along with your responses in your assignment submission.

References: At least 3 scholarly sources (the course resources count as references)

Your answers should demonstrate thoughtful consideration of the ideas and concepts that are presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect graduate-level writing and APA standards. Be sure to adhere to Northcentral University’s Academic Integrity Policy.

Upload your document and click the *Submit to Dropbox *button

Week 1 – Assignment 2: Examine the Basic Layout and Functions of SPSS

You will now have the opportunity to become familiar with the basic layout and functions of SPSS using descriptive statistics.

Open SPSS, and then open the data file “grades.sav” from this week’s resources.

Use the *Variable View* tab found in the lower center of the window to answer the following questions:

- How many variables are in this dataset? SPSS uses the word
*scale*for both interval and ratio data. - How many of the variables in this dataset are scale, nominal, and ordinal variables?

Use the *Data View* tab found in the lower left-hand corner of the window to answer the following questions:

- How many subjects are in this dataset?
- What are the last name, gender, and GPA of the 18th subject?

Conduct a simple analysis and retrieve some output:

- In the
*Menu Commands,*click on*Analyze*to open a drop-down window. - From the drop-down window, open the
*Descriptive Statistics*window, then*Descriptive….* - A dialog window will open
*Descriptive*. Locate and move GPA into the*Variables**Box*.

Click on the *Options *tab on the right-hand side of the *Variables Box. *Another dialog window will open, *Descriptive: Options.*

In this dialog box, select: Mean, Standard Deviation, Range, and S.E. Mean. Click *Continue* to close this box.

- Click
*OK*in the Descriptive dialog box.

Then, answer these questions:

- What is the number of GPAs?
- What is the range?
- What is the mean?
- What is the standard error?
- What is the standard deviation?

Please write a short paragraph (APA style) which includes a brief description of the dataset (variables included in the dataset), the number of subjects, and the mean and standard deviation of the dataset.

Length: 1-2 pages including output table, answers to five questions, and paragraph. Please include the question prompts along with your responses in your assignment submission. In addition to a WORD (.doc) file with the answers to the assignment questions, also include the output (.spv) file. (*NOTE*: SPSS automatically generates the .spv file as you work in SPSS. When you close your SPSS main window, SPSS will ask you if you want to save the output file. Click ‘yes’, then save to your computer and upload with your assignment.)

References: No references are required, though any sources used other than those provided within the assignment should be cited and referenced in APA format

Your answers should demonstrate thoughtful consideration of the ideas and concepts that are presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect graduate-level writing and APA standards. Be sure to adhere to Northcentral University’s Academic Integrity Policy.

Upload your document and click the *Submit to Dropbox *button.

Any statistical software provides you the opportunity to create graphs and visually depict the data and the results of your analyses. This week, you will create several different types of graphs and provide examples of different graphs.

**NCU SOE faculty have created two helpful videos to guide you through this assignment. Please see this week’s resources to view the videos.**

In this SPSS assignment, you will increase your understanding of graphs and frequency distributions as well as their value when interpreting data. Complete the following steps and include your responses to submit to your professor:

- Using the data in Table 1, where the grade is your factor and the score is your outcome variable, open a new SPSS file and enter the data. Then using the graph tab, then legacy dialogs, create the following graphs and include them in your submission.
- line graph
- bar chart
- pie chart

**Table 1**

*Data for Step 1 of Assignment*

Grade | Score |

1 | 45 |

2 | 56 |

3 | 49 |

4 | 57 |

5 | 61 |

6 | 72 |

- Discuss which of these graphs (line, bar, pie) present these data better.

**Frequency Distributions**

The file ** SPSSExam.sav** contains data regarding students’ performance on an SPSS exam. Four variables were measured:

**exam**(first year SPSS exam score as a percentage),

**computer**(measure of computer literacy in percent),

**lecture**(percentage of SPSS lectures attended), and

**numeracy**(a measure of numerical ability out of 15). There is a variable called

**uni**indicating whether the students attended World University, Universe University, Planet University, and Cosmos University.

- Create two bar charts: one bar chart with sex (biological sex) in the x-axis and one bar chart with the university on the x-axis. Include these charts in your submission.
- Create two frequency distribution tables for sex and university attended. Include these tables in your submission and answer the following questions.
- What percentage of the sample is male and female?
- What percentage of the sample attended World U, Universe U, Planet U, and Cosmos U?

- For computer literacy, numerical ability, and lectures attended create three frequency distribution tables with their respective histograms. Include these tables with your submission and provide the following information.
- Computer Literacy
- Numeracy
- Lectures Attended
- Describe the shape of the frequency distributions.
- Differentiate between the frequency, percent, valid percent, and cumulative percent columns.

- Please discuss when it is appropriate to use a bar chart and when it is appropriate to use a histogram to display data (keep in mind the level of measurement of the variables).

Remember that there are additional Supplemental Resources available for each week in the Course Resources linked at the top of your course.

Length: Complete responses to all parts of all six prompts. In addition to a WORD (.doc) file with the answers to the assignment questions, also include the output (.spv) file. (*NOTE*: SPSS automatically generates the .spv file as you work in SPSS. When you close your SPSS main window, SPSS will ask you if you want to save the output file. Click ‘yes’, then save to your computer and upload with your assignment.)

References: At least 3 scholarly sources (the course resources count as references).

Your answers should demonstrate thoughtful consideration of the ideas and concepts that are presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect graduate-level writing and APA standards. Be sure to adhere to Northcentral University’s Academic Integrity Policy.

Upload your document and click the *Submit to Dropbox *button.

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Week 3 – Assignment: Analyze Central Tendency and Variability

This assignment includes four variables that indicate the students’ performances on an SPSS exam. You will find the information in the SPSS file named *SPSSExam.sav*. You can find this file from your resources used in Week 2.

The four variables measured were:

*exam*(first-year SPSS exam score as a percentage)*computer*(measure of computer literacy in percent)*lecture*(percentage of SPSS lectures attended)*numeracy*(a measure of numerical ability out of 15)

In the data, there is a variable calledUni. This variable indicates the university the students attended. The four universities are World University, Universe University, Planet University, and Cosmos University.

**NCU SOE faculty have created a helpful video to guide you through this assignment. Please see this week’s resources to view the video.**

The goal of this assignment is to explore the concepts related to central tendency and variability for both categorical and continuous variables. Furthermore, another goal is for you to explore the various tools for data analysis in the SPSS software.

- Split the file by gender. Calculate the mean and standard deviation of
*exam*and*lectures*for males and females.*Hint: use*Explore*found under the*ANALYSIS => Descriptive*tabs, exam and lectures will be the dependent variable and sex will be the factor.* - Compute the mean, median, and mode for
*computer*(computer literacy).- What value is the most representative measure of the central tendency for this variable and why?

- Calculate the range and the standard deviation for
*computer*(computer literacy).- What does the range tell you about the data?
- What does the standard deviation tell you about the data?

- Create a frequency distribution table and a graph for Uni (university).
- What is the most appropriate measure of central tendency?
- Please provide a rationale for why you selected this measure of central tendency for this variable.

Remember that there are additional Supplemental Resources available for each week in the Course Resources linked at the top of your course.

Length: Complete responses to all parts of all four questions. Please include the question prompts along with your responses in your assignment submission. In addition to a WORD (.doc) file with the answers to the assignment questions, also include the output (.spv) file. (*NOTE*: SPSS automatically generates the .spv file as you work in SPSS. When you close your SPSS main window, SPSS will ask you if you want to save the output file. Click ‘yes’, then save to your computer and upload with your assignment.)

References: No references are required, though any sources used other than those provided within the assignment should be cited and referenced in APA format

Your answers should demonstrate thoughtful consideration of the ideas and concepts presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards. Be sure to adhere to Northcentral University’s Academic Integrity Policy.

Upload your document and click the *Submit to Dropbox *button.

Week 4 – Assignment: Examine the Normal Curve and Calculate Standard Scores

The goal of this assignment is to explore the concepts related to the normal curve and standard scores. Furthermore, another goal is for you to explore the various tools for data analysis in the SPSS software. These tools include the *compute* and *standardize scores* functions. You will find the steps in the assignment instructions to use these tools.

**NCU SOE faculty have created two helpful videos to guide you through this assignment. Please see this week’s resources to view the videos.**

Remember that there are additional Supplemental Resources available for each week in the Course Resources linked at the top of your course.

Use the data from four science assignments provided in Table 2.

**Table 2**

*Data from four science assignments*

Student | A1 | A2 | A3 | A4 |

1 | 97 | 28 | 89 | 9 |

2 | 94 | 86 | 80 | 39 |

3 | 95 | 80 | 82 | 10 |

4 | 97 | 39 | 83 | 14 |

5 | 96 | 60 | 87 | 38 |

6 | 95 | 42 | 84 | 34 |

7 | 94 | 38 | 85 | 31 |

8 | 95 | 60 | 85 | 21 |

9 | 98 | 62 | 84 | 12 |

10 | 96 | 51 | 83 | 20 |

11 | 96 | 53 | 86 | 38 |

12 | 98 | 32 | 85 | 27 |

Part I:

Please enter the following data in SPSS and perform the necessary analyses in SPSS to answer the following questions.

- Once data have been entered, calculate descriptive statistics (central tendency and variability) for each of the assignment scores.
- What level of measurement do the data represent (i.e., nominal, ordinal, interval, ratio)?
- What is the mean and standard deviation for each assignment score?
- What is the median for each assignment score?
- What is the mode for each assignment score?
- What is the range for each assignment score?

Part II:

- Your first task is to obtain a total assignment score for each student. To obtain the total score (“totscore”), you will use the
*compute*tool in SPSS. To do this, in the top menu click on*Transform*, then*Compute*.- A
*compute variable*box will appear, where you can type in a formula for the program to calculate. - In the
*target variable*box, enter “totscore.” Then, click once in the*numeric expression*box. - After that, double click on
*Assignment 1*, to move it from the list of variables to the numeric expression box. - Then click on the + (plus) sign.
- After that, double click on
*Assignment 2*and follow the same instructions as Assignment 1 for the rest of the assignments. This new variable is the total sum of the four assignment scores.

- A
- The second step is to calculate a z-score for each of the assignments and the total score.
- To create the z-score in SPSS, you will go to
*analyze*, then*descriptive statistics*, and*descriptive*. - Include in the window the four assignments and the “totscore” variables. Then check the box on
*Save Standardized Values as Variables*.

- To create the z-score in SPSS, you will go to
- The third step is to convert each of the scores to a t-score.
- The equation to a t-score is 50+(10*z-score). To convert the scores to t-score you will use the compute tool again.
- To do this, in the top menu click on
*Transform*, then*Compute*. - A
*compute variable*box will appear, where you can type in a formula for the program to calculate. - In the
*target variable*box, enter the t-score1. - In the
*numeric expression*box, enter the t-score equation 50+(10*ZA_1) and use each appropriate z-score for each assignment. You also need a total t-score (tot_tscore) for each student. - Use
*Transform*, then*Compute*. - Enter (tot_tscore) as the target variable and insert a formula in the
*Numeric Expression*window to sum the four t-scores.

- In a separate document (Word or Excel), create two columns to compare the totscores (total scores) and the tot tscores (total t-scores). Please use the following grade breakdown to rank the assignment grade scores 1 through 12, where 1 is the highest score A, and 12 the lowest score F:
- A to rank 1
- B to rank 2
- B– to rank 3
- C+ to rank 4
- C to ranks 5, 6, 7, and 8
- C– to rank 9
- D+ to rank 10
- D to rank 11
- F to rank 12

- Answer questions 7 through 13

- Determine what is unusual about student 1’s performances on the tests.
- What is strange about student 2’s performances? How do the performances of these two students differ, and how are they the same?
- What grades would be assigned to these two students if the total of the raw scores were used to determine grades?
- What grades would be assigned to these two students if the total of the t-scores were used to determine grades?
- Why are your answers to questions 9 and 10 different? (
*Hint: examine the variability of the tests*) - What are the means and the standard deviations the four z-scores distributions, to one decimal point?
- What are the means and standard deviations of the four t-score distributions, to one decimal point?

Length: Complete responses to all parts of all 13 questions. Please include the question prompts along with your responses in your assignment submission. In addition to a WORD (.doc) file with the answers to the assignment questions, also include the output (.spv) file. (*NOTE*: SPSS automatically generates the .spv file as you work in SPSS. When you close your SPSS main window, SPSS will ask you if you want to save the output file. Click ‘yes’, then save to your computer and upload with your assignment.)

References: No references are required, though any sources used other than those provided within the assignment should be cited and referenced in APA format

Your responses should demonstrate thoughtful consideration of the ideas and concepts presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards. Be sure to adhere to Northcentral University’s Academic Integrity Policy.

Upload your document and click the *Submit to Dropbox *button.

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Part I. Inferential Statistics Concepts and Assumptions & Concepts

- What is the standard error of measurement?
- What is the standard error of the mean?
- Please discuss the term confidence interval.
- What are four main assumptions for parametric statistics?
- Please discuss and explain in your own words each of the four main assumptions.
- Why it is important to discuss or test the assumptions before conducting parametric statistical analyses?

Part II. Standard Error of the Mean and Confidence Intervals

A district-wide test is used to measure math aptitude in freshmen in high school students, with a mean of 78 and a standard deviation of 12. Thirty-six selected freshmen took the test, and their mean score was 85. You are tasked to examine if these students are significantly different from the district test group.

- Calculate the standard error of the mean (SEM)?
- After calculating the SEM, create a 95% confidence interval?
- After calculating the SEM, create a 99% confidence interval?
- Do these students have a similar or better score than the rest of the district students?

Part III. Testing for Parametric Assumptions

A movie company wants to test if there are movies that are preferred more by females and preferred more by males. The movie company surveyed 20 men and 20 women and showed half of each sample a film that was supposed to be a movie preferred more by females (*The Notebook*) and males (*The Godfather*). In all cases, the movie company measured their excitement as an indicator of how much they enjoyed the film. Please open the *movie* SPSS file, and answer the following questions:

- Conduct the required analyses to test for the assumptions of normality (Shapiro-Wilks or Kolmogorov-Smirnov) and homogeneity of the variance (Levene’s) for the two films from the data in the
*movie*data file. - Please write a few sentences describing the assumptions required in this exercise and whether or not they were met. Please include information from the output to support your answers.

Length: Complete responses to all questions in all three parts. Please include the question prompts along with your responses in your assignment submission. In addition to a WORD (.doc) file with the answers to the assignment questions, also include the output (.spv) file. (*NOTE*: SPSS automatically generates the .spv file as you work in SPSS. When you close your SPSS main window, SPSS will ask you if you want to save the output file. Click ‘yes’, then save to your computer and upload with your assignment.)

Your responses should demonstrate thoughtful consideration of the ideas and concepts presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards. Be sure to adhere to Northcentral University’s Academic Integrity Policy.

Upload your document and click the *Submit to Dropbox *button.

This assignment has two parts. Part I is about correlation and regression. Part II is about chi-square. Include both parts in a single document.

**NCU SOE faculty have created helpful videos to guide you through this assignment. Please see this week’s resources to view all of the videos.**

Part I. Correlation and Regression

Imagine a researcher is interested in examining the relationship of self-esteem (*Self_Estm*) and productivity (*Prod*). The researcher is also interested in the ability to predict the productivity of teachers using years of teaching (Experience) as the predicting variable.

Use the *teacher’data.sav* dataset available in this week’s resources (and Table 3) to conduct the analysis involving *Self_estm*, *Prod*, and *Experienc*e. Use these data to answer the questions.

**Table 3**

*Dataset **teacher’data.sav *

Sex | Self_Estm | Experience | Prod |

M | 64 | 25 | 25 |

M | 68 | 14 | 28 |

F | 74 | 10 | 36 |

M | 75 | 20 | 38 |

F | 76 | 30 | 34 |

F | 79 | 3 | 36 |

F | 82 | 13 | 42 |

M | 68 | 29 | 22 |

M | 70 | 19 | 38 |

F | 74 | 22 | 39 |

F | 76 | 6 | 34 |

F | 78 | 16 | 38 |

M | 81 | 15 | 45 |

M | 85 | 2 | 46 |

F | 71 | 15 | 30 |

M | 73 | 12 | 34 |

F | 76 | 18 | 33 |

M | 77 | 10 | 36 |

M | 78 | 21 | 38 |

M | 80 | 5 | 42 |

F | 83 | 18 | 46 |

F | 86 | 21 | 49 |

F | 74 | 15 | 38 |

M | 77 | 18 | 32 |

M | 77 | 12 | 35 |

F | 78 | 8 | 36 |

F | 84 | 32 | 49 |

F | 87 | 16 | 48 |

F | 77 | 29 | 36 |

M | 71 | 19 | 33 |

F | 75 | 4 | 33 |

F | 76 | 17 | 36 |

M | 79 | 30 | 38 |

M | 83 | 20 | 48 |

F | 89 | 11 | 48 |

F | 92 | 14 | 49 |

In this assignment, you will expand your understanding of inferential statistics involving correlation and regression. Complete the following:

1. Produce an SPSS analysis for a correlation between participants’ self-esteem and productivity.

- Provide the null and alternative hypotheses. (
*Hint: The relationship between variables.*) - Discuss the difference between the Pearson correlation and the Spearman correlation. Explain when it is appropriate to use one of the other. (
*Hint: Level of measurement of the variables.*) - Determine if a Pearson correlation or Spearman correlation will be used and explain why.
- Which is the measure for effect size used in a correlation analysis?
- What is the effect size in this correlation analysis? Explain whether it is small, medium, or large.
- Report the results in APA format. (
*Hint: Follow the guidelines in the APA manual to report statistical result*. Only the statistical analysis results are needed; no additional discussion or explanation needed.) - What decision can be made from these results regarding the null hypothesis?

2. Produce an SPSS analysis using regression to examine the impact of participants’ years of experience on their productivity.

- Provide the null and alternative hypotheses. (
*Hint: This is related to prediction.*) - Which is the measure for effect size used in a regression analysis?
- What is the effect size in this regression analysis? Explain whether it is small, medium, or large.
- Report the results in APA format. (
*Hint: Follow the guidelines in the APA manual to report statistical results*.) - What decision can be made from these results regarding the null hypothesis? Be sure to consider possible study limitations and provide recommendations for future research.
- Given only two variables were examined, how does testing the significance of the regression equation relate to testing the significance of the Pearson correlation?

Part II. Chi-Square

You will be entering and analyzing in SPSS the data in Table 4. When entering the data, please use 1 for Red, 2 for Yellow, and 3 for Green. Make sure that you go to the variable view window and enter these values in the label box.

Twenty senior students were asked to choose the color they preferred for their senior-class shirt. Conduct a chi-square goodness-of-fit test to test the null hypothesis that says there is no true difference in the population from which the sample was drawn.

**Table 4**

*Red, Yellow, and Green Data*

Student | Color | Color Code |

1 | Red | 1 |

2 | Yellow | 2 |

3 | Green | 3 |

4 | Red | 1 |

5 | Red | 1 |

6 | Yellow | 2 |

7 | Yellow | 2 |

8 | Yellow | 2 |

9 | Yellow | 2 |

10 | Red | 1 |

11 | Yellow | 2 |

12 | Green | 3 |

13 | Red | 1 |

14 | Yellow | 2 |

15 | Yellow | 2 |

16 | Yellow | 2 |

17 | Yellow | 2 |

18 | Yellow | 2 |

19 | Yellow | 2 |

20 | Green | 3 |

- Please provide the null and alternative hypothesis for this variable.
- Please provide the observed value
*n*for Red. - Please provide the observed value
*n*for Yellow. - Please provide the observed value
*n*Green. - Please provide the expected value for each of the colors.
- Please provide the value of the chi-square test.
- Please provide the value of the associated probability (sig.). Are the results significant at the .05 level?
- Write a statement of the results of the significance test in APA style (make sure to include your decision based on the statistical hypothesis).

Length: Complete responses for all parts of all questions in both parts. In addition to a WORD (.doc) file with the answers to the assignment questions, also include the output (.spv) file. (*NOTE*: SPSS automatically generates the .spv file as you work in SPSS. When you close your SPSS main window, SPSS will ask you if you want to save the output file. Click ‘yes’, then save to your computer and upload with your assignment.)

Your responses should demonstrate thoughtful consideration of the ideas and concepts presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards. Be sure to adhere to Northcentral University’s Academic Integrity Policy.

Upload your document and click the *Submit to Dropbox *button.

**ORDER A CUSTOM-WRITTEN, PLAGIARISM-FREE PAPER HERE**

Part I. Paired Samples *t* – test

Please enter and analyze the data in the table below in SPSS with appropriate *t* – test analysis. These data contain changes in self-esteem scores from pretest (before psychological counseling) to posttest (after psychological counseling).

**Table 5**

*Depression Scale Pretest and Posttest Scores*

Participant | Pretest | Posttest |

1 | 30 | 28 |

2 | 33 | 29 |

3 | 29 | 30 |

4 | 27 | 31 |

5 | 26 | 29 |

6 | 37 | 37 |

7 | 40 | 41 |

8 | 35 | 40 |

9 | 36 | 37 |

10 | 35 | 38 |

- What are the two main assumptions underlying the repeated-measures
*t*– test? Determine if the assumptions are met. - Please produce an SPSS output for the paired-samples
*t*– test comparing the pre- and posttest scores. - Provide the null and alternative hypothesis.
- What are the mean and standard deviation for beginning pretest and end posttest? (Please use APA style.)
- What is the value of the
*t*statistic? - What is the mean difference?
- What is the standard deviation difference?
- What is the value of Cohen’s d? Is it small, medium, or large?
- What might be concluded from these results? (
*Hint: The decision about the null hypothesis.*)

Part II. Independent Samples *t* – test

The experimental group received instruction in calculus via the Internet, while the control group received traditional classroom instruction. The data in Table 6 consist of the final examination scores for both groups. Conduct an independent-samples *t* – test, and then answer the questions that follow.

**Table 6**

*Independent Samples t – test data*

Group | Code | Exam |

Experimental | 1 | 30 |

Control | 2 | 28 |

Control | 2 | 33 |

Experimental | 1 | 26 |

Experimental | 1 | 34 |

Control | 2 | 34 |

Experimental | 1 | 37 |

Control | 2 | 33 |

Experimental | 1 | 26 |

Control | 2 | 26 |

- There are three main assumptions needing to be satisfied before using the independent-samples
*t*– test for testing differences between the genders.- Use SPSS to generate the output needed to test the assumptions.
- Please discuss each one and explain whether each assumption has been met using SPSS output as needed to include the Shapiro-Wilk test for normality (used when the sample size is less than 50), histograms, and the Levene’s test.
- Keep in mind if the population value is unknown, it is permissible to infer from sample values. Regardless of sample size, test whether these assumptions are met.

- Please produce an SPSS output for an independent-samples
*t*– test comparing the experimental and control group in the calculus exam score. - What are the null and alternative hypotheses?
- What is the mean for the experimental group?
- What is the mean for the control group?
- What is the value of
*t*? - What is the associated probability?
- Report the results in APA format.
- What might be concluded from this hypothetical study? (Hint: the decision about the null hypothesis)

Part III. Analysis of Variance

You will be entering and analyzing in SPSS the data in Table 7. The data contain estimated hours of Internet usage for samples from three socioeconomic status (SES) groups. Name the first variable *SES*and label it “Socioeconomic Status.”Use the value labels of 3 = High SES, 2 = Middle SES, and 1 = Low SES. Name the dependent variable *Internet*and label it “Hours of Internet Usage (Weekly).”

**Table 7**

*Analysis of Variance data*

Participant | SES | Codes | Hours |

1 | High | 3 | 10 |

2 | High | 3 | 12 |

3 | High | 3 | 11 |

4 | High | 3 | 15 |

5 | Middle | 2 | 14 |

6 | Middle | 2 | 13 |

7 | Middle | 2 | 10 |

8 | Middle | 2 | 12 |

9 | Low | 1 | 9 |

10 | Low | 1 | 11 |

11 | Low | 1 | 8 |

12 | Low | 1 | 12 |

- Using SPSS, conduct a one-way ANOVA to test for differences in hours of Internet usage between the different SES groups. After conducting the ANOVA using SPSS, be sure to present the findings in the SPSS table format.
- What is the mean for the low-SES group?
- What is the mean for the middle-SES group?
- What is the mean for the high-SES group?
- What is the
*F*value? - What is the value of the associated probability?
- Report the results in a narrative using APA format.
- What can be concluded from these results? (
*Hint: The decision about the null hypothesis.*)

Length: Complete responses to all questions in all three parts. In addition to a WORD (.doc) file with the answers to the assignment questions, also include the output (.spv) file. (*NOTE*: SPSS automatically generates the .spv file as you work in SPSS. When you close your SPSS main window, SPSS will ask you if you want to save the output file. Click ‘yes’, then save to your computer and upload with your assignment.)

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Week 8 – Signature Assignment: Develop a Statistical Analysis Plan

To complete this Signature Assignment, you will use the statistical knowledge and scientific writing skills acquired in this course. You will be initially asked to develop two types of research questions, or research questions involving relationships between variables and research questions involving the difference between variables.

A research question is a clear inquiry asking just one question and eliciting more than a simple yes or no response. Begin your research question with *how*, *why*, or *what *rather than *does*, *do*, or *can*. Once your research questions have been developed, you will need to create corresponding null and alternative hypotheses for each research question. Remember, the null hypothesis indicates a non-significant relationship or difference will exist while an alternative hypothesis indicates a significant relationship or difference will exist.

Research questions and hypotheses are divided into two categories: relationship questions and descriptive questions.

Relationship research questions include comparison (difference questions) and strength of association (associational):

*Difference*research questions are used when comparing scores (on the dependent variable) on two or more groups. These questions attempt to demonstrate that groups are not the same on the dependent variable.*Association*research questions are used when the researcher wants to examine the association or relationship between variables. The approach is commonly used to see how two or more variables covary (vary together). For example, do higher values on one variable correspond to higher values on the other? These questions are also used to how one or more variables can be used to predict another variable.

Descriptiveresearch questions do not use inferential statistics. Descriptive questions are used to summarize or describe the current data. No generalization to a larger population of individuals.

For example:

Research Question 1:

Q: What is the relationship between family socioeconomic level and student state-mandated test performance?

Ho: A non-significant relationship will exist between family socioeconomic level and student state-mandated test performance.

Ha: A significant relationship will exist between family socioeconomic level and student state-mandated test performance.

Research Question 2:

Q: What is the relationship between family socioeconomic level, gender, and student state-mandated test performance?

Ho: A non-significant relationship will exist between family socioeconomic level, gender, and student state-mandated test performance.

Ha: A significant relationship will exist between family socioeconomic level, gender, and student state-mandated test performance.

Research Question 3:

Q: What is the effect of an intensive language immersion program on spoken English acquisition skills among high school ESL students?

Ho: An intensive language immersion program will result in a non-significant effect on spoken English acquisition skills among high school ESL students.

Ha: An intensive language immersion program will result in a significant effect on spoken English acquisition skills among high school ESL students.

Research Question 4:

Q: What is the effect of an intensive language immersion program on spoken English acquisition skills among high school ESL students by gender?

Ho: An intensive language immersion program will result in a non-significant effect on spoken English acquisition skills among high school ESL students by gender.

Ha: An intensive language immersion program will result in a significant effect on spoken English acquisition skills among high school ESL students by gender.

You will then need to explain the type of statistical analysis to be employed to analyze the relationships and effects between variables. Keep in mind, a statistical relationship analysis involving two variables often involves a Pearson *r* correlation or a simple regression while a statistical relationship analysis involving three or more variables often involves multiple correlations—or what is more widely known as multiple regression. A statistical analysis testing for effect involving two variables often involves some form of a *t* – test; on the other hand, a statistical analysis of effect involving three or more variables often involves some form of an ANOVA.

Carefully review the scenario and research questions provided below for you to develop the statistical analyses plans.

**Scenario:**

You are the new director of institutional research at a small state university, and you have been assigned the task of analyzing information for the dean of the School of Education regarding the performance of their undergraduate students on the often-controversial Graduate Record Exam (GRE). Many educators believe the GRE is a poor evaluator of undergraduate performance as well as a poor predictor of graduate school performance. The dean is considering eliminating the GRE from graduate school admissions requirements.

The dean has already collected data on four variables: 1) gender, 2) grade point average (GPA), 3) GRE score, and 4) graduate degree completion frequency. Your job is to develop a proposed analysis to assist the dean to make an informed decision regarding the future use of the GRE.

You should also discuss the assumptions of each test. No data, calculations, or actual statistical results are required to be presented. This is similar to a question that you will encounter in your Doctoral Comprehensive Exams. You should provide information that shows your understanding of the different types of analyses, as well as possible outcomes of the analyses. In addition, you have to include in your discussion the possible conclusions based on the possible results: rejecting the null and not rejecting the null.

Using this information, develop the following foundational components for a proposed analysis. In your proposal, you will compose four research questions and discuss the proposed analyses of the data to answer the research questions. For each research question, you need to address:

- Corresponding null and alternative hypotheses.
- Type of statistical analysis to be employed to determine the significance.
- Assumptions of each test.
- Explanations of potential outcomes identifying both non-significant and significant relationships as related to both null and alternative hypotheses. Note that no data, calculations, or results are needed.
- Recommendations based on non-significant and significant findings.

The four types of research questions are:

- A
**relationship**research question involving GPA and GRE scores. - A
**relationship**research question involving gender, GPA, and GRE scores. - An
**effect**research question involving gender and GRE scores. - An
**effect**research question involving gender, GRE score, and degree completion frequency.

Finally, complete your analysis plan with a written discussion of your potential outcomes and recommendations for the dean based on your findings.

Length: 4–5 pages, not including references and title page.

References: 5 scholarly sources

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