S-012Empirical Methods: Introduction

to Statistics for Research

Fall 2011-2012

Harvard Graduate School of Education

• Tuesday and Thursday, 11:30 -1:00pm

• Askwith Lecture Hall (Longfellow 100)

• Terrence Tivnan

• Larsen Hall 415

• tivnante@gse.harvard.edu

S-012 Introduction to statistics

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• Provides an introduction. There are no special prerequisites.

• Many of you have had some background, but lots of variation.

• Focus is on understanding and applying the concepts (not on formulas or computations)

• Examples from education, easily adapted to other fields

• The more you learn, the more fun statistics is

• Consider S-030 as a follow-up

S-012 Introduction to statistics

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• Hinkle, D.E., Wiersma, W., and Jurs, S.G. (2003). Applied statistics for the behavioral sciences (5th edition). Boston: Houghton Mifflin.

• Publication Manual of the American Psychological Association, Sixth edition. Washington, DC: American Psychological Association.

• Nicol, A. A. & Pexman, P. M. (1999). Presenting your findings: A practical guide for creating tables. Washington, DC: American Psychological Association.

Textbooks

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• Stata software

• Available on machines throughout GSE

• Runs on Mac and Windows-based machines• Easy to get started. Great with advanced features.

• Similar features to many other packages– SPSS– SAS– Minitab

• Used in advanced courses here at GSE

• Acock, A. (2008) A gentle introduction to Stata, Second edition. College Station, TX: Stata Press.

Computer software

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• Six formal required assignments• All involve reporting and interpreting results• Emphasis on clear writing, not on computations

• Assignment Approximate weight

• 1 5

• 2 10

• 3 20

• 4 25

• 5 15

• 6 25

• Letter grade or the SAT/No credit option

Assignments

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• Practice problems will help to review and reinforce many of the basic concepts.

• These are drawn from the textbook, and will also be posted on the course website

• Not graded

• We will review these during optional weekly review sessions

Optional practice problems

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• Weekly office hours schedule available soon

• Scheduled throughout the week

• We will also hold some Virtual Office Hours via the internet

• We will assign you to a TF who will keep track of your assignments, checking them in and returning them to you

• TFs will also help with weekly review sessions.

• TFs are very helpful resources!

Teaching Fellows

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• No course pack for S-012

• I will distribute packages of handouts

• Be sure to bring these to class

• Available on line via the S-012 course website

Class handouts

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• All regular class sessions will be recorded and made available via the course website

• This is a great resource

• We may also record some of the review sessions

Class videos

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• We will have clickers available to pick up at the beginning of class

• I ask questions (via Power Point slides)

• You can select your answer

• We see a graph of the results

• A way to make the class a bit more interactive

• A way to get feedback– For students

– For me

In-class instant polls

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• Unit 1: Basic data sets and descriptive statistics

• Unit 2: Properties of distributions– Normal curve, interpreting probabilities, confidence intervals

• Unit 3: Techniques for comparing groups– Hypothesis testing– T-tests for means, F-test for variances– Using and interpreting effect sizes

• Unit 4: Comparing groups– Categorical data and measures of association– ANOVA

• Unit 5: Correlation and Regression

Course topics

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Unit 1: Getting familiar with a data set1A: Descriptive Statistics

Class Date Topics

1 Sept 1Describing a data set. Types of data. Measures of central

tendency and variability. Trimmed and weighted means.

2 Sept 6

Measures of variability—the range, variance and standard deviation. A formula for the standard deviation. Notation for sample statistics and population parameters. Stem-and-leaf displays. Finding the median and the quartiles. Using box plots for comparing groups. Rules for outliers—the RUB and RLB.

3 Sept 8

Shapes of distributions. Key vocabulary: Bell-shaped, bi-modal, uniform, skewness and kurtosis. Transforming scores to different scales. Raw scores, percentages, ranking. The z transformation, the square root transformation and the log transformation.

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Unit 2: Properties of distributions

4 Sept 13Interpreting means and standard deviations when there is a

bell-shaped distribution. The empirical rules. Using the table of normal-curve areas. Finding percentiles.

5 Sept 15

Applying the normal-curve rules—an example of comparing three schools. The distribution of sample means—how different samples tend to vary. The mean and standard deviation of the distribution or sample means.

6 Sept 20More on the distribution of sample means. The Central Limit

Theorem. Finding probabilities for results from samples.

7 Sept 22Constructing confidence intervals for sample means. Levels

of confidence. Interpreting confidence intervals.

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Unit 3: Techniques for comparing groups

8 Sept 27 An introduction to the t-distribution. Using the t-table to construct confidence intervals. Importing data files for use in Stata.

9 Sept 29 Testing hypotheses using t. The CI approach and the NHST approach. The null and alternative hypotheses. The critical values of t. Comparing two samples. Looking at some Stata output.

10 Oct 4 More details on using the t-test for comparing two groups. The pooled approach and the Satterthwaite approach. The F-test for the variances. Looking at the output.

11 Oct 6 More practice reading and interpreting the output. Setting up confidence intervals for proportions (when we have binary or dichotomous variables). An example of early reading data: gender differences and school differences.

12 Oct 11 A nonparametric test for comparing groups—the Wilcoxon rank-sum test. A test for analyzing changes over time—the “paired t-test” for repeated measures.

13 Oct 13 Examples of effect sizes in journal articles.15

Comparing groupsCategorical data

Class Date Topics

14 Oct 18Analyzing categorical data. The CI approach. The z-test to compare

two samples. The chi-square test. The steps in the test. Seeing the output.

15 Oct 20

Analyzing data in contingency tables. Reading the row percentages and the column percentages. Looking at the results of the chi-square test. Comparing larger tables. Comparing more than two groups.

16 Oct 25

APA guidelines for constructing helpful tables. Measures of association for categorical data. Controlling for third variables by examining separate subtables. Bayes theorem and conditional probabilities.

17 Oct 27More ideas for categorical data: Yates’s continuity-adjusted

chisquare, Fisher’s Exact Test and “The Lady Tasting Tea” example, McNemar’s chi-square test for change.

18 Nov 1

The chisquare “goodness of fit” test. Testing the shapes of distributions. Planned (orthogonal) and pair-wise contrasts after an overall chisquare test. Revisiting assignment 3 -- creating categorical variables and comparing the neighborhoods using chisquare tests and the rank-sum test.

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Comparing groupsAnalysis of variance

Class Date Topics

19 Nov 3

Analysis of variance for comparing two or more groups. One-way ANOVA and pair-wise contrasts. Two-way ANOVA, looking for main effects and interactions. The equivalence of t-test and ANOVA when comparing two groups.

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Correlation

Class Date Topics

20 Nov 8Introduction to correlation. The correlation coefficient.

Looking at plots. The correlation matrix.

21 Nov 10

Formulas for the correlation coefficient. The t-test of significance. Looking at internal consistency using Cronbach’s alpha. Correlation examples from research journals.

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Regression

22 Nov 15 Introduction to regression. Looking at trends. The slope and the intercept. The regression coefficients. Plotting the predicted values. Looking at residuals. The tests of the coefficients.

23 Nov 17 Regression assumptions—linearity, normality, homoscedasticity, no causation. Using R-square as a measure. The “proportion of variance” explanation. Revisiting the electricity data from assignment 4 and looking at some correlation and regression results.

24 Nov 22 The formulas for regression. The SAS commands for PROC PLOT ; and PROC REG ; Finding the “best predictor.” Checking R-square. The F-test for R-square.. A multiple regression example.

Nov 25 Holiday! No class today!

25 Nov 29 Checking and interpreting the regression coefficients. The t-test for the coefficients. Examples of regression coefficients in journal articles

26 Dec 1 More practice with regression. Predicting annual incomes. Interpreting coefficients. Looking at R-square. A multiple regression example.

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• Final regular class on December 1

• Assignment 6 due on Thursday, December 8

End of the course

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