EDPSY Chp. 2: Measurement and Statistical Notation

Populations vs. Samples Population –The complete set of individuals Characteristics are called parameters Sample –A subset of the population Characteristics are called statistics. –In most cases we cannot study all the members of a population

Descriptive vs. Inferential Descriptive statistics –Summarize/organize a group of numbers from a research study Inferential statistics –Draw conclusions/make inferences that go beyond the numbers from a research study –Determine if a causal relationship exists between the IV and DV

Common Research Designs Correlational –Do two qualities “go together”. Comparing intact groups –a.k.a. causal-comparative and ex post facto designs. Quasi-experiments –Researcher manipulates IV True experiments –Must have random assignment. Why? –Researcher manipulates IV

Variables –Characteristics that takes on different values Achievement Age Condition –Independent variable (IV) Manipulated or Experimental –Condition Subject –Personality –Gender –Dependent variable (DV) The outcome of interest –Achievement –Drop-out status

Measurement Is the assignment of numerals to objects. Nominal –Examples: Gender, party affiliation, and place of birth Ordinal –Examples: SES, Student rank, and Place in race Interval –Examples: Test scores, personality and attitude scales. Ratio –Examples: Weight, length, reaction time, and number of responses

Categorical, Continuous and Discontinuous Categorical (nominal) –Gender, party affiliation, etc. Discontinuous –No intermediate values Children, deaths, accidents, etc. Continuous –Variable may assume an value Age, weight, blood sugar, etc.

Values Exhaustive –Must be able to assign a value to all objects. Mutually Exclusive –Each object can only be assigned one of a set of values. A variable with only one value is not a variable. –It is a constant.

Chapter 2: Statistical Notation Nouns, Adjectives, Verbs and Adverbs. –Say what? Here’s what you need to know –X X i = a specific observation –N # of observations –∑ Sigma –Means to sum –Work from left to right Perform operations in parentheses first Exponentiation and square roots Perform summing operations Simplify numerator and divisor Multiplication and division Addition and subtraction

Pop Quiz (non graded) –In groups of three or four Perform the indicated operations. What was that?

Chapter 3 Exploratory Data Analysis

A set of tools to help us exam data –Visually representing data makes it easy to see patterns. 49, 10, 8, 26, 16, 18, 47, 41, 45, 36, 12, 42, 46, 6, 4, 23, 2, 43, 35, 32 –Can you see a pattern in the above data? Imagine if the data set was larger. –100 cases –1000 cases

Three goals Central tendency –What is the most common score? –What number best represents the data? Dispersion –What is the spread of the scores? What is the shape of the distribution?

Frequency Tables Let say a teacher gives her students a spelling test and wants to understand the distribution of the resultant scores. –5, 4, 6, 3, 5, 7, 2, 4, 3, 4 ValueFCumulative F%Cum% 71110% % % 43730%70% 32920%90% %100% N=10

As groups Create a frequency table using the following values. –20, 19, 17, 16, 15, 14, 12, 11, 10, 9

Banded Intervals A.k.a. Grouped frequency tables With the previous data the frequency table did not help. –Why? Solution: Create intervals Try building a table using the following intervals <=13, 14 – 18, 19+

Stem-and-leaf plots Babe Ruth –Hit the following number of Home Runs from 1920 – , 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22 –As a group let’ build a stem and leaf plot –With two classes’ spelling scores on a 50 item test. Class 1: 49, 46, 42, 38, 34, 33, 32, 30, 29, 25 Class 2: 39, 38, 38, 36, 36, 31, 29, 29, 28, 19 –As a group let’ build a stem and leaf plot

Landmarks in the data Quartiles –We’re often interested in the 25 th, 50 th and 75 th percentiles. 39, 38, 38, 36, 36, 31, 29, 29, 28, 19 –Steps First, order the scores from least to greatest. Second, Add 1 to the sample size. –Why? Third, Multiply sample size by percentile to find location. –Q1 = (10 + 1) *.25 –Q2 = (10 + 1) *.50 –Q3 = (10 + 1) *.75 »If the value obtained is a fraction take the average of the two adjacent X values.

Box-and-Whiskers Plots (a.k.a., Boxplots)

Shapes of Distributions Normal distribution Positive Skew –Or right skewed Negative Skew –Or left skewed

How is this variable distributed?

Descriptive Statistics

Statistics vs. Parameters A parameter is a characteristic of a population. –It is a numerical or graphic way to summarize data obtained from the population A statistic is a characteristic of a sample. –It is a numerical or graphic way to summarize data obtained from a sample

Types of Numerical Data There are two fundamental types of numerical data: 1) Categorical data: obtained by determining the frequency of occurrences in each of several categories 2) Quantitative data: obtained by determining placement on a scale that indicates amount or degree

Measures of Central Tendency Central Tendency Average (Mean)MedianMode

Mean (Arithmetic Mean) Mean (arithmetic mean) of data values –Sample mean –Population mean Sample Size Population Size

Mean The most common measure of central tendency Affected by extreme values (outliers) Mean = 5Mean = 6

Median Robust measure of central tendency Not affected by extreme values In an Ordered array, median is the “middle” number –If n or N is odd, median is the middle number –If n or N is even, median is the average of the two middle numbers Median = 5

Mode A measure of central tendency Value that occurs most often Not affected by extreme values Used for either numerical or categorical data There may may be no mode There may be several modes Mode = No Mode