Week 5 ETEC 668 Quantitative Research in Educational Technology Dr. Seungoh Paek February 12, 2014

Tonight’s Agenda Continuing SPSS Introduction to PSPP Introduction to RStudio Introduction to Probability Group Discussion for Research Paper

Continuing Week 4

Using SPSS

Using SPSS

Sigma Freud & Descriptive Statistics A Picture is Really Worth a Thousand Words

Histograms with Polygon Hand Drawn Histogram

Cool Ways to Chart Data Line Chart

Cool Ways to Chart Data Pie Chart

Using the Computer to Illustrate Data Creating Histogram Graphs

Using the Computer to Illustrate Data Creating Bar Graphs

Using the Computer to Illustrate Data Creating Line Graphs

Using the Computer to Illustrate Data Creating Pie Graphs

A Taste of PSPP

Download PSPP - For Mac, click here. For Window, click here.

A TASTE of RSTudio

R R is a free software environment for statistical computing and graphics.

RStudio RStudio is a free and open source integrated development environment (IDE) for R, a programming language for statistical computing and graphics.

Probability, Samples, Bell Curve, z Scores, Hypotheses, Hypothesis Testing, & significance Chapter 7 & Chapter 8

Probability

Why Probability? Describe and predict what we don’t know from current data Basis for the Degree of confidence a Hypothesis is “true” statistical significance

Examples Flip a coin Role a Die Flip 2 coins 2 possible outcomes Heads or Tails 50% chance each Role a Die 6 possible outcomes 1 – 2 – 3 – 4 – 5 – 6 16.6% chance each Flip 2 coins How many possible outcomes? What % chance for each?

Examples Flip 2 coins 4 possible outcomes 25% chance each 1 2 3 4 Coin A Coin B 1 2 3 4 Flip 2 coins 4 possible outcomes 25% chance each

Sample v Population

Definitions Population Sample The large group to which you would like to generalize your findings Sample The smaller, representative group of the population used for research.

Characteristics of a sample Needs to be representative Truly random = representative = unbiased Sampling error – how well the sample represents the population Size matters – larger sample = more representative

Mathematical Symbols Mean Standard Deviation Variance Number of Cases Population = μ Sample = X Standard Deviation Population = σ Sample = SD Variance Population = σ2 Sample = SD2 Number of Cases Population = N Sample = n

The Normal Curve

The Normal curve

More Normal Curve

About Normal Curve Almost all scores fall between -3 and +3 SD from mean 99.74% Specific percentages between points on x-axis 2 or more normal curves can be compared

Normal Curve and Percents

z Scores

The z Score The number of standard deviations from the mean Negative scores are below (left of) the mean Positive scores are above (right of) the mean

= The z Score Standard Score Allows you to compare apples and oranges The probability of a score occurring =

Hypotheses

What is a Hypothesis? An “educated guess” Direct extension of the question Translates problem or research question into a testable form Two types Null Hypothesis Research Hypothesis

A Good Hypothesis Declarative statement Expected relationship between variables Reflection of theory/literature Brief, to the point Testable

Why a Null Hypothesis? No amount of experimentation can ever prove me right; a single experiment can prove me wrong. ~ Albert Einstein

The Null Hypothesis Statement of no relationship Two things are equal H0 : μA = μB Refers to Population Indirectly tested

The Research Hypothesis Definite Statement Relationship exists between variables Two types Nondirectional - H1 : XA ≠ XB Directional - H1 : X1 > X2 Refers to sample Directly tested

Hypothesis Testing

Hypothesis Testing All events have a probability associated with them p = your guess of chance p < .05 .05 or 5% in Education and Psychology 5% likelihood of results occurring by chance alone

Error types Type I Type II Reject H0 when you should not Fail to reject H0 when you should

Error Table Investigator’s Decision H0 is True H0 is False Reject H0 The Real Situation (Unknown to investigator) Investigator’s Decision H0 is True H0 is False Reject H0 Type I error Correct decision Do Not reject H0 Type II error

Significance

Statistical Based on probability Research was technically successful H0 was rejected P value Education p < .05 = 5% chance Medical p < .01 or .001 = 1% or .1% chance

Practical Does it mean anything to the population? Is that new treatment worth the cost? Are my students really doing that much better?

Questions?

Stating the Research Question February 12, 2014

Where are we now? Identified a problem focus Familiar with the literature Next step – determine specific questions for your research study Research questions provide the basis for planning research study – design, materials, data analysis

Can meaningful learning be enhanced by using a computer to personalize math word problems for each student?

Research Questions vs Research Hypotheses

Research Questions in Qualitative Research Preferred when little is known about a phenomenon Used when previous studies report conflicting results Used to describe phenomena

Research Hypotheses for Quantitative Research Educated guess or presumption based on literature States the nature of the relationship between two or more variables Predicts the research outcome Research study designed to test the relationship described in the hypothesis .

Null Hypotheses Implicit complementary statement to the research hypothesis States no relationship/difference exists between variables Statistical test performed on the null Assumed to be true until support for the research hypothesis is demonstrated

Alternative Hypotheses Directional hypothesis Precise statement indicating the nature and direction of the relationship/difference between variables Nondirectional hypothesis States only that relationship/difference will occur

Assessing Hypotheses Simply stated? Single sentence? At least two variables? Variables clearly stated? Is the relationship/difference precisely stated? Testable?

Types of Variables Variable Element that is identified in the hypothesis or research question Property or characteristic of people or things that varies in quality or magnitude Must be identified as independent or dependent

Independent Variables (IV) Manipulation or variation of this variable is the cause of change in other variables Technically, independent variable is the term reserved for experimental studies Also called antecedent variable, experimental variable, treatment variable, causal variable, predictor variable

Dependent Variables (DV) The variable of primary interest Research question/hypothesis describes, explains, or predicts changes in it The variable that is influenced or changed by the independent variable In non-experimental research, also called criterion variable, outcome variable

Intervening or Mediating Variables Intervening/Mediating variable Presumed to explain or provide a link between independent and dependent variables Relationship between the IV and DV can only be explained when the intervening variable is present E.g. effect of study prep on test scores Organization of study ideas into a framework (intervening/mediating)

Control Variables Special type of IV that can potentially influence the DV Use statistical procedures (e.g. analysis covariance) to control for these variables May be demographic or personal variables that need to be “controlled” so that true influence of IV on DV can be determined

Confounding Variables Confuses or obscures the effect of independent on dependent Makes it difficult to isolate the effects of the independent variable Typically cannot be directly measured or observed Researchers comment on the influence after study is completed

Relationship Between Independent and Dependent Variables Cannot specify independent variables without specifying dependent variables Number of independent and dependent variables depends on the nature and complexity of the study The number and type of variables dictates which statistical test will be used

Model for Writing Descriptive Questions & Hypotheses Identify IV, DV & any intervening/moderating variables Specify descriptive questions for each IV, DV & intervening variable Write inferential questions that relate variables or compare groups

Scenario A researcher wants to study the relationship of critical thinking skills to student achievement in science classes for 8th-graders in a large metropolitan school district. The researcher controls for the effects of prior grades in science classes and parents’ educational attainment.

Step 1: Identify variables What is the IV?

Step 1: Identify variables What is the IV? Critical thinking skills (measured on an instrument)

Step 1: Identify variables What is the DV?

Step 1: Identify variables What is the DV? Student achievement (measured by grades)

Step 1: Identify variables What are the control variables?

Step 1: Identify variables What are the control variables? Prior grades in science class Educational attainment of parents

Descriptive Questions How do the students rate on critical thinking skills? What are the students’ achievement grades in science classes? What are the students’ prior grades in science classes? What is the educational attainment of the parents of the 8th graders?

Inferential Questions Does critical thinking ability relate to student achievement? Does critical thinking ability relate to student achievement, controlling for the effects of prior grades in science and the educational attainment of the 8th-graders’ parents?

What to do Week 5 Do the required readings for Week 06. Salkind, N. J. Chapter 16. Redicting Who’ll Win the Super Bowl: Using Linear Regression Salkind, N. J. Chapter 20. The Ten (or More) Best Internet Sites for Statistics Stuff Continue the group discussion on the final research paper, and post the 1) literature review outline and 2) research questions for your paper to the Forum in Laulima (Due by Tuesday, February 18th).