Overview of the course, review of the syllabus.

Install the Excel Data Analysis Tool Pack.

Peruse this website: Become familiar with the content of the various pages and sections.

Introduction to the online statistics textbooks and other resources: 

Pedhaser and Schmelkin text

VassarStats

HyperStat Online,

StatTrek

Research Methods Knowledge Base

Trying out the Excel Data Analysis ToolPac

Before the next session, complete the following:

Order the Pedhazur and Schmelkin text.

Point your browser to the Vassar Stats online textbook and read Chapters 1 and 2.

Be sure you can articulate the differences between various scales of measurement: nominal, ordinal, interval, and ratio. Be prepared to differentiate between the notions of reliability and validity of measures and measuring instruments. Pay attention to the discussions of variables in the text.

Statistics deals with several types of distributions, some imperial (i.e., manifest) and some theoretical.  Be sure you know the difference. Distributions are the subject of Chapter 2.  Also, know how to describe a distribution in terms of measures of central tendency, variability, and skew. In this chapter you will encounter terms such as deviation scores, mean-squared deviation, sums of squares, samples, populations, statistics, parameters, and so forth. These are all important terms in statistics-- understanding these terms is critical to continuing in this course. When I talk about sums of squares, or SS, for instance, you should know that I am talking about.

Then, go to the Foundations Chapter (in the Table of Contents) in the Research Methods Knowledge Base and read the section on the Language of Research.

Having read this section, you should be in a position to:

• articulate the difference between theoretical and empirical research,

• understand why research in the social sciences is probabilistic,

• explain why most social research is concerned with uncovering causal relaitionships,

• describe the three types of research questions addressed in research studies,

• explain the role time plays in research design,

• articulate the differences linear and curvilinear relationships,

• explain what researchers mean when they talk about variables,

• talk intelligently about hypotheses, including the difference between a null and alternative hypothesis,

• explain the difference statisticians make between qualitative and quantitative variables,

• tell why it is important, in a research study, to differentiate the unit of analysis, and 

• differentiate between the ecological and exception fallacies.

Since the unit of analysis plays such a critical role in research design, here is a brief paper on Unit of Analysis that is well worth your reading.  

Discussion of Assigned Readings

Using Excel to compute various descriptive statistics.

Introduction to Probability, Probability Distributions and Calculators

Before the next session (Jan. 28), complete the following:

Read Chapters 4 & 5 in HyperStat Online. 

In Chapter 4, in the Subsection on the Binominal distribution.

In Chapter 5, Subsection 4 (Converting to Percentiles) tryout the z-calculator.

Also, in Chapter 5, Subsection 5 (Area Under a Portion of the Normal Curve), check out, and try using, the z table.

Also read Chapters 5 & 6 in the Vassar Stats online textbook.

Check out the Binomial Probability Calculator in the Appendix to Chapter 5. 

Download my short paper on Summation Operators and complete (to be turned in the next time we meet) the exercises at the end of the paper.

    Read my Paper on Probability and Probability Distributions.

Review and Discussion of the previous week's assignments.

Answers to the exercises at the end of the paper on Summation Operators can be found HERE.

Solve the probability problem given HERE. (The answer can be found HERE)

Before the next session (Feb. 4), complete the following:

Assuming you have acquired a copy of the Pedhazur and Schmelkin (P&S) text: read the Overview and Chapters 1-5 in P&S ( You can skip the exercises; we will read Chapter 6 later in the course).

Read Chapter 1 in the Vassar Stats online textbook.

In RMKB, in the chapter on Measurement, read the sections on Construct Validity, Reliability, and Levels of Measurement. Since measurement is one of the basic tools of research and statistics, the chapter is critically important. This chapter complements Chapter 1 in the Vassar Stats online textbook.

The subsection on Construct Validity discusses several types of validity, threats to validity, and various approaches for establishing validity. All doctoral students should be familiar with these concepts.

The subsections on Reliability, and Levels of Measurement (which repeats some of the material covered earlier) also, are critically important.

Class activity:

Discussion of the role measurement plays in social science research.

The article, Procedures for estimating internal consistency reliability, prepared by the Iowa Technical Adequacy Project (ITAP) describes Coefficient Alpha and how to compute it. The article also shows how to use Excel to compute Coefficient Alpha. If you find yourselves, later, constructing an instrument, or even using an existing instrument, to measure some attribute, you will need to know how to compute internal consistency reliability.

I once used a Motivations for Reading instrument to measure elementary school students interest in reading. The instrument can be found HERE, and an Excel file containing the responses, HERE.

Use the guidelines given in the Procedures article to compute the alpha-reliability of my administration of the Motivations for Reading instrument.

Before next week (when there is no physical class meeiting) complete the following:

Before we can dig into statistical analysis, we need to first understand research designs (here I refer to qualitative research designs, of course.) In preparation, begin by reading Chapters 7-10 in P&S and the sections on Internal Validity and Introduction to Design under the Chapter on Design in RMKB

Before next week: 

Read Chapters 11-14 in P&S and the several sections under the Chapter on Design in RMKB.

Choose an area or topic research interest and locate, in the literature, three articles related to that area or topic: one each representing experimental (or quasi-experimental) research, correlational (or nonexperimental) research. Bring copies (or summaries) of the articles to class next week.

Class activity: 

Discussion of the role research design plays in research.

Distinguish among experimental, quasi-experimental, and nonexperimental research designs.

Review and discussion of articles.

Work on a solution to the Problem given HERE. (Answer)

Threats to the Validity of a study

Type I and Type II Errors

Before next week

Next week we move into what is generally considered the heart of statistics: testing hypotheses about population parameters.

We do this using sample statistics. I say this because we are never interested in the obtained value of sample statistics themselves. Instead we are interested in what the sample statistics tell us about the population parameters. 

In preparation, read the following:

The sections on Conclusion Validity, Data Preparation and Descriptive Statistics in the Chapter on Analysis in RMKB.

Chapters 1, 2, and 3 in Hyperstat.

Class Activity: Using Various Software for Testing Hypotheses of Differences (Parametric and Nonparametric Tests)

Tests for comparing two independent samples

Student t Test for Independent Samples

Mann-Whitney U Test

Wilcoxon Independent Samples Test

Tests for comparing two dependent samples

Student t test for dependent samples

Use the Sign Test to perform a non-parametric solution to the t test scenario given in the previous example. Again, try programming the test in Excel.

Wilcoxon matched pairs signed ranks test to analyze the same data. (One solution is given HERE.)

You can find Excel solutions to some of these problems HERE.

Before the next session, complete the following:

The following scenario/problem has been placed on the ning as Forum, "Class Example 1." Go to the ning and solve the problem presented there. Use what we covered in class earlier this week.

Two weeks ago you were given the following assignment

Choose an area or topic research interest and locate, in the literature, three articles related to that area or topic: one each representing experimental (or quasi-experimental) research, correlational (or nonexperimental) research. Bring copies (or summaries) of the articles to class next week.

Using this worksheet, give the characteristics of the study. Print a copy and bring it with you to class next week.

Read Chapters 9-12 in the Vassar Stats online textbook and

chapters 7 - 10 in Hyperstat.

Class Activity: More on Hypothesis Testing  

You began exploring tests for hypothesis last week. Here, you will be led through a few additional scenarios using procedures available on the web as well as Excel. 

For instance, suppose we are interested in the lunch-time caloric intake at lunchtime among middle school students. Obviously, we cannot measure this for ALL middle school students. Instead, we take a representative (usually random) sample of middle school students and measure their caloric intake at lunchtime, compute the average (a statistic) and use this as an estimate of the caloric intake of all students.

Suppose we have data that a healthy lunchtime caloric intake for average middle school students is 700 calories (I don't really know how accurate this is). If the average caloric intake of our sample of middle school students is 850 calories, can we conclude that the population from which our sample was drawn is eating, on average, too many calories at lunchtime? This is a problem in statistical inference and requires an hypothesis test. (Data can be found HERE.)

In-class problem to be developed.

By the end of this week, complete the following:  

In  HyperStat Online, read the chapters on Estimation (Chapters 7 & 8) and Hypothesis Testing (Chapter 9).

In the chapter on Estimation, make sure you have a firm grasp of the concept of a standard error and margin of error.

Know how to compute the variance the standard error of the mean and a confidence interval around a mean.

In the chapter on Hypothesis Testing: pay close attention to the section on Foundations of Testing. Know how to test whether a sample mean is equal to some predetermined value, and test the difference between independent means and dependent (paired) means.

You may find the discussion found at the following links particularly useful in understanding this chapter. 

HYPOTHESIS TESTING,

ONE AND TWO-TAILED t-TESTS,

ERRORS IN HYPOTHESIS TESTING,  and

Testing Hypotheses About Single Means

Also, in the Chapter on Hypothesis Testing, understand and know how to compute the power of a statistical test.

Finally, in this chapter, be able to differentiate among situations where a chi-square test is appropriate for testing goodness of fit, homogeneity, and independence.

May 11.

Class Activity: 

Today we will  compute, and interpret, a one-way analysis of variance using Excel, Vassar Stats, SPSS.

First, however, before using SPSS go to Instructional Stuff for Statistics and click on Formatting SPSS Tables. Then, follow the instructions depending upon whether you have SPSS version 15 or lower or 16 or higher. This will format your SPSS tables to look like APA tables.

For these examples we will use the scenario found HERE and the data found HERE.

We will begin with Excel, using the ToolPac. (You can find my Excel solution HERE.)

Next, we'll analyze the data win Vassar Stats.

Next, we analyze the data using SPSS. Here is the Syntax.

My write up of the results can  be found HERE.

Before the next session, complete the following:

Read the following: 

My Introduction to Factorial Analysis of Variance and my brief paper on Partitioning Sums of Squares in ANOVA 

Chapter 13 in HyperStat Online  and Chapter 16 in the Vassar Stats online textbook.

What to pay attention to in the HyperstatOnline chapter on Factorial Between-subjects ANOVA: Section 1, Basic definitions, does a good job at explaining factorial designs including main effects and interaction effects. This section is not mathematical; read this section carefully. Section 2 introduces you to an ANOVA Table and its major components: Degrees of Freedom, Sums of Squares, Mean Squares, and F ratios, and significance levels (Probability Levels.) The last part of Section 2 extends the discussion from two-factor ANOVA to three-factor ANOVA. Follow the example described in the section. Section 3 elaborates on the interpretation of ANOVA results, beginning with a discussion of main effects and interaction effects. I discusses when additional analyses are needed following a statistically significant interaction. It includes a discussion of simple effects, which you need to understand.  Section 4 is particularly important. I will help you understand how to report the results of a factorial ANOVA. Section includes some rather simple exercises for you to attempt. The two numerical example can be computed using the Excel or with the Two-Way Factorial ANOVA for Independent Samples  procedure in Vassar Stats--or with SPSS. What to pay attention to in the Vassar Stats chapter: In Chapter 16 (Two-Way Analysis of Variance for Independent Samples)  spend enough time on Part 1 so that you feel you have a good understanding of it (especially the partitioning of Total Sums of Squares, SST, into the two component Sums of Squares: Between (SSBG) and Within (SSWG). In Part 2 you do not have to worry too much about the computational stuff...again, just concentrate on understanding the manipulation of Sums of Squares. You do not need to dwell on the "conceptual," "tentative," and "computational" sections. Do, however, pay attention to the sections df, MS, F, and the sampling distribution of F. In Part 3, read the description of the example (you can browse over the computational stuff), but be sure to examine, and make sure you understand, the graphs showing means for main effects and the interaction. Also, read the sections on DF, MS values, F ratios, the Sampling Distribution of F and the explanation of results. In Part 4, read the introduction to the example. This example extends the 2 x 2 ANOVA of a 2 (rows) x 3 (columns) factorial ANOVA. You can browse over the computational stuff (make sure you understand the graphs) in the middle of the page. Pay attention to the last table describing the main effects and interaction. The last paragraph on the page is important. Think about what that paragraph is telling you. Part 5 addresses some of the important assumptions behind the use of ANOVA. You should have a good grasp of what is being said in the discussion. You do not have to read the final section in Part 5: Step-by-Step Computational Procedure.

Class Activity: Solve the problem found HERE.

My solution to this exercise can be found HERE (you can also get a PDF copy).

By the end of this week, complete the following:

Read my brief General Overview of Regression Analysis, and

Chapters 15 and 16 in HyperStat Online.

Class Activity

Reopen Howell 13-2

Using Excel, VassarStats and SPSS to compute:

Correlation

Pearson Product Moment Correlation (r_xy).

Spearman Rho (ρ_xy) Correlation.

Chi square (χ²).

Regression Analysis of ANOVA data 

By the end of this week, complete the following:

Read the following:

Chapter 3, including the appendices, in the Vassar Stats online textbook, and my Introduction to Linear Regression Analysis.

Class activity:  

Regression Analysis

Prediction
Explanation

Before the next time we meet (Apr 15), complete the following:

Re-read my paper, Introduction to Linear Regression Analysis.

Continuation of Regression analysis discussion and application.

Before the next time we meet (Apr 22), complete the following:

Read Chapters 15 in the Vassar Stats online textbook.

Class activity:  

Using SPSS and VassarStats to compute a Repeated Measures ANCOVA.

An updated paper on Dummy, Effect, and Orthogonal Coding is now available.

Class activity:

Repeated Measures and Randomized Blocks ANOVA:  Example