1. PY 427 Statistics 1Fall 2006 Kin Ching Kong, Ph.D Lecture 1 Chicago School of Professional Psychology

2. Agenda Syllabus Math Review The Big Picture Why Do We Need Statistics? What is Statistics? Statistical Terminology Scales of Measurement Statistical Notation

3. Math Review 3 + 2 x 7 = 2 x (5 - 2 2 ) = (3 + 2) x 7 = 12/4 + 2 = 2 x (5 - 2) 2 = (6+6)/(4 + 2) 2 = Express 1/10 as a: percentage: decimal: Express 1% as a: decimal: fraction: Express.05 as a: fraction: percentage: In a group of 80 students, 20% are psych. majors. How many psych. Majors are in the group? 3 + (-2) + (-1) + 4 = 6 - (-2) = 4 x (-3) = (-16)/8 = -2 x (-6) = (-100)/(-4) = Find X: X + 6 = 13, X = X – 14 = 15, X = 3X = 12, X = X/5 = 3, X = 3X + 5 = -4, X = (X + 3)/2 = 14, X = 3 2 = square root of 9 = Square root of (5 2 ) = If a=3 and b= -1, then a 2 b 3 =

4. Math Review Answers Link

5. The Big Picture Why Do We Need Statistics? What Is Statistics?  facts & figures  Statistical procedures (mathematical procedures for organizing, summarizing, and interpreting information)

6. Statistical Terminology Population & Sample Parameter & Statistic Descriptive Statistics Inferential Statistics Sampling Error Variable & Constant Independent & Dependent Variables Discrete & Continuous Variables

7. Populations & Samples Population: all the individuals of interest in a particular study Sample: a subset of the population, usually selected to represent the population. Illustration of the relationship between population & sample (Fig. 1.1, p4 of your book) Illustration of the relationship between population & sample

8. Parameters & Statistics Parameter: a value, usually a numerical value, that describes a population. Statistic: a value, usually a numerical value, that describes a sample. Parameters are usually identified by Greek letters Statistics are usually identified by English letters

9. Descriptive Statistics Data: measurements or observations (scores or raw scores) A Data Set: a collection of measurements or observations Descriptive Statistics: statistical procedures that are used to summarize, organize, and simplify data.

10. Inferential Statistics Inferential Statistics: statistical procedures that allow us to study samples and then make generalization about the population from which they were selected. Sampling Error: the discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter. Illustration of Sampling Error (fig. 1.2, p.7 of your book) Illustration of Sampling Error

11. Variable & Constant Constant: a characteristic or condition that does not change or vary, but is the same for every individual. (e.g. # of minutes in an hour, graduate school of every students in this class, the number 7) Variable: a characteristic or condition that changes or takes on different values for different individuals. (e.g. height, weight, age, scores on an exam or rating scale) Discrete Variable: consists of separate, indivisible categories. Now values can exist between two neighboring categories. (e.g. number of children) Continuous Variable: there are an infinite number of possible values that fall between any two observed values. (e.g. height, weight) Measurement of Continuous Variable Each score is really an interval with boundaries defined by the real limits. Real Limit: halfway between adjacent scores

12. Independent & Dependent Variables Two Major Class of Variables in Research: Independent Variable (IV): a variable manipulated by the researcher (e.g. amount of food fed to each group of lab rats) a participant variable used to create groups (e.g. gender) a variable that predicts another variable (e.g. hours of study in predicting grade) Dependent Variable (DV): the variable that is observed for changes in order to assess the effect of the treatment (e.g. how fast the rats ran the maze to find food) the variable that is measured in comparing two or more groups (e.g. average income of male and female) the variable that is predicted by the dependent variable (e.g. grade of the students) You can think of the relationship between independent and dependent variables as: the independent variable precedes the dependent variable the independent variable predicts the dependent variable the independent variable causes the dependent variable

13. An Example Research Question: Does teaching method A and teaching method B differ in their effectiveness in teaching reading to first-grade students? Independent Variable: Teaching Method Dependent Variable: scores on a standardized reading test given 6 months after the reading programs. Constant: students’ grade Population: all first-grade students Illustration of this study (fig. 1.3, p8 of your book) Illustration of this study

14. Scales of Measurement Nominal Scale: a set of categories with different names. Nominal scale does not make quantitative distinctions between the categories (e.g. gender) Ordinal Scale: a set of categories that are organized in an ordered sequence. Interval Scale: consists of ordered categories that are all intervals of exactly the same size. Equal differences between numbers on the scale reflect equal differences in magnitude. However, ratios of magnitudes are not meaningful. Ratio Scale: is an interval scale with the additional feature of an absolute zero point. With a ratio scale, ratios of numbers do reflect ratios of magnitude.

15. Statistical Notation X, Y often used to represent variables. N = number of scores, or individuals in the population of interest. n = number of scores, or individuals in the sample Summation Notation: sigma  Order of Mathematical Operations: Parentheses Squaring, exponents Multiplying, dividing Summation using the sigma notation Addition or subtraction