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

igma 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

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– 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?

• Flip 2 coins– How many possible outcomes?– What % chance for each?

Examples

• Flip 2 coins– 4 possible outcomes– 25% chance each

Outcome Coin A Coin B

1

2

3

4

Sample v Population

Definitions

Population– 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 – 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 chancep < .05

– .05 or 5% in Education and Psychology– 5% likelihood of results occurring by chance

alone

Error types

Type I– Reject H0 when you should not

Type II– Fail to reject H0 when you should

Error Table

The Real Situation

(Unknown to investigator)

Investigator’s Decision

H0 is True H0 is False

Reject H0 Type I errorCorrect decision

Do Not reject H0Correct decision

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 phenomenonUsed when previous studies report conflicting resultsUsed 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

Confounding variable– 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 variablesNumber of independent and dependent variables depends on the nature and complexity of the studyThe 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

1. 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

2. 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).