S-012 Empirical Methods: Introduction to Statistics for Research Fall Harvard Graduate School of Education

Tuesday and Thursday, 11:30 -1:00pm Askwith Lecture Hall (Longfellow 100) Terrence Tivnan Larsen Hall 415 S-012 Introduction to statistics 2

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 3

Hinkle, D.E., Wiersma, W., and Jurs, S.G. (2003). Applied statistics for the behavioral sciences (5th edition). Boston: Houghton Mifflin. Textbooks 4 Some students prefer to use a text book. Here is a good one. Other textbooks are also okay. You may have one that you prefer. Most basic statistics textbooks will cover the important topics. Earlier editions are perfectly fine. Lots of on-line resources are also helpful. Many students do fine without a textbook Other textbooks are also okay. You may have one that you prefer. Most basic statistics textbooks will cover the important topics. Earlier editions are perfectly fine. Lots of on-line resources are also helpful. Many students do fine without a textbook This text includes lots of practice problems from a wide variety of areas – education, psychology, etc. So it provides lots of practice.

Stata software Available on machines throughout GSE 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. (2014) A gentle introduction to Stata, Fourth edition. College Station, TX: Stata Press. Computer software Earlier editions perfectly fine. There are lots of great on-line help resources for Stata Earlier editions perfectly fine. There are lots of great on-line help resources for Stata

Six formal required assignments All involve reporting and interpreting results Emphasis on clear writing, not on computations AssignmentApproximate weight Letter grade or the SAT/No credit option Assignments 6

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 7

Weekly office hours schedule available soon Scheduled throughout the week We may 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 The TFs will give you lots of help and feedback TFs are very helpful resources! Teaching Fellows 8

No course pack for S-012 I will distribute packages of course materials Be sure to bring these to class Available on line via the S-012 course website Class handouts 9

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 10

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 11

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 12

Unit 1: Getting familiar with a data set 1A: Descriptive Statistics ClassDateTopics 1Sept 4 Describing a data set. Types of data. Measures of central tendency and variability. Trimmed and weighted means. 2Sept 9 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. 3Sept 11 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. 13

Unit 2: Properties of distributions 4Sept 16 Interpreting means and standard deviations when there is a bell-shaped distribution. The empirical rules. Using the table of normal-curve areas. Finding percentiles. 5Sept 18 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. 6Sept 23 More on the distribution of sample means. The Central Limit Theorem. Finding probabilities for results from samples. 7Sept 28 Constructing confidence intervals for sample means. Levels of confidence. Interpreting confidence intervals. 14

Unit 3: Techniques for comparing groups 8Sept 30An introduction to the t-distribution. Using the t-table to construct confidence intervals. Importing data files for use in Stata. 9Oct 2Testing 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. 10Oct 7More 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. 11Oct 9More 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. 12Oct 14A nonparametric test for comparing groups—the Wilcoxon rank-sum test. A test for analyzing changes over time—the “paired t-test” for repeated measures. 13Oct 16Examples of effect sizes in journal articles. 15

Comparing groups Categorical data ClassDateTopics 14Oct 21 Analyzing categorical data. The CI approach. The z-test to compare two samples. The chi-square test. The steps in the test. Seeing the output. 15Oct 23 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. 16Oct 28 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. 17Oct 30 More 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. 18Nov 4 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. 16

Comparing groups Analysis of variance ClassDateTopics 19Nov 6 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. 17

Correlation ClassDateTopics 20Nov 13 Introduction to correlation. The correlation coefficient. Looking at plots. The correlation matrix. 21Nov 18 Formulas for the correlation coefficient. The t-test of significance. Looking at internal consistency using Cronbach’s alpha. Correlation examples from research journals. 18

Regression 22Nov 20Introduction 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. 23Nov 25Regression 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. --Nov 27Holiday! No class today! 24Dec 2Checking and interpreting the regression coefficients. The t-test for the coefficients. Examples of regression coefficients in journal articles.. Predicting annual incomes. A multiple regression example 19

Final regular class on December 2 Assignment 6 due on Thursday, December 11 End of the course 20