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Edpsy 511 Basic concepts Exploratory Data Analysis 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 Random Sampling vs. Random Assignment • Simple random sampling – Each member of the population has an equal likelihood of being selected. • Helps ensure that our sample will represent the population of interest. • Random assignment – Assigning subjects to different conditions in a way that they have equal chance of being placed in either condition. • Controls for confounding Goals of Scientific Research • Exploratory – What is out there? • Descriptive – What does this group look like? • Explanatory – Why and how are these constructs related? • Evaluation – Does this program work? • Prediction – Who will become depressed? 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 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. Statistical Notation • Nouns, Adjectives, Verbs and Adverbs. – • Say what? Here’s what you need to know – X • – Xi = 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 N X i 1 i • Pop Quiz (non graded) – In groups of three or four • Perform the indicated operations. • What was that? N X ( X ) 2 N ( N 1) 2 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 Value F Cumulative F % Cum% 7 1 1 10% 10% 6 1 2 10% 20% 5 2 4 20% 40% 4 3 7 30% 70% 3 2 9 20% 90% 2 1 10 10% 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 – 1934. • 54, 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 25th, 50th and 75th 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? 3.0 2.5 Frequency 2.0 1.5 1.0 0.5 Mean = 4.3 Std. Dev. = 1.494 N = 10 0.0 1 2 3 4 5 score 6 7 8 How is this variable distributed? 3.0 2.5 Frequency 2.0 1.5 1.0 0.5 Mean = 2.80 Std. Dev. = 1.75119 N = 10 0.0 0.00 1.00 2.00 3.00 4.00 right 5.00 6.00 7.00 How is this variable distributed? 3.0 2.5 Frequency 2.0 1.5 1.0 0.5 Mean = 5.40 Std. Dev. = 1.42984 N = 10 0.0 2.00 3.00 4.00 5.00 left 6.00 7.00 8.00 A little on SPSS • The assignments require hand calculations and SPSS practice – Typically I have you check your answers using SPSS – Do not buy SPSS – Do not leave the SPSS work for night before the due date. – You will need a TEC center account • Do that after class today