introduction to basic statistical tools for research oced 5443 interpreting research in oced dr....

Introduction to Basic Statistical Tools for Research


OCED 5443

Interpreting Research in OCED

Dr. Ausburn

OCED 5443

Interpreting Research in OCED

Dr. Ausburn

No One Panic!No One Panic!• We are not going to calculate anything• We are not going to delve into statistical

intricacies• We are going to see how some important

statistics are used and reported in research• We are going to focus on how to interpret

reported statistics• We are going to look carefully at examples of

every statistic we talk about• We are going to talk it over until you

understand

Good Data Makes You a….Good Data Makes You a….

Research Star!

Descriptive Statistics

(Non-Inferential)

Summary Snapshot of

Sample


(Non-Inferential)

Summary Snapshot of

Sample

Measures of Central Tendency

(How Data “Clusters”)

• Mean (X) – Group’s Arithmetic “average”

• Mode (Mo) – Number appearing most frequently in group

• Median (Md) – Point that splits the group in half; the group’s midpoint


(Non-Inferential)

Summary Snapshot of

Sample


(Non-Inferential)

Summary Snapshot of

Sample

Measures of Dispersion(How Data “Spreads”)

• Range – Difference between highest point and lowest point in group – Exclusive (high – low)– Inclusive (high – low + 1)

• Quartile Deviation (Semi-Interquartile Range) – Spread off the Median

• Variance (s2) – Spread off the Mean– Based on “deviation scores” (score –

mean of scores)– Deviation score = deviation of score from

the mean– Variance represents random (“error”)

variation of scores within a group– Used in many inferential statistics

• Standard Deviation (s or sd) – Spread off the Mean– Positive square root of the variance– Sort of an “average” deviation from the

Mean– Important statistically due to relationship

to Mean and Normal Distribution Curve


(Non-Inferential)

Summary Snapshot of

Sample


(Non-Inferential)

Summary Snapshot of

Sample

Measure of Distribution(How Data is Grouped)

• Frequency distribution– Usually presented in a

frequency table or graph– Data divided into

categories– Number of people in group

who fall into each category = “frequency” (ƒ)


(Non-Inferential)

Summary Snapshot of

Sample


(Non-Inferential)

Summary Snapshot of

Sample

Measures of Relationship(How Variables Rise and

Fall Together)• Correlation Coefficients (r,

rxxx, R) – Numerous types; choice depends on

types of data being correlated– Requires 2 sets of data on 1 group of

people; 2 measures on same people– Values between 0 and 1; may be

positive or negative– Strength/Magnitude = how close to 1– Direction = + or –– Shows only relationship: How the 2

variables “vary together”– Does NOT imply causality, much less

direction of causality!


(Non-Inferential)

Summary Snapshot of

POPULATION


(Non-Inferential)

Summary Snapshot of

POPULATION

Describing a Population is just like describing a

Sample

• Measures of Central Tendency (pop. Mean= )

• Measures of Dispersion(pop. variance/sd = and 2)

• Frequency Distributions• Correlation Coefficients

A measure on a sample is called a statistic

A measure on a population is called a parameter

Inferential Statistics

• Tests of significance

• Hypothesis testing

• Infer from sample to population

Comparisons of Frequency Distributions

Chi-Square (2) Tests

- Several variations

- Data must be in frequencies (ƒ)

- Compare “observed” ƒs to “expected” ƒs

Chi-Square Tests:Interpreting the “Answer”

2 = value of chi-square

df = degrees of freedom for the test will be listed

p = or p < or p > = or < or > (or % level) %, probability or alpha level will be listed

Interpretation? Let’s look at example and see what this all means


Testing and Predicting Relationships among

Variables• Correlation coefficients

– Same types and rules used for descriptive purposes

– Remember: Correlation does not imply causality

• Regression analysis– Linear regression– Multiple regression

• Cluster analysis• Factor analysis





Testing Means for Significant Differences

• t-test (or “student’s t”)• Analysis of Variance (ANOVA)

or F-test• Variations on ANOVA for

special circumstances• Non-parametric versions for

some samples that won’t meet assumptions of t and F





• Must have only:– 1 independent variable– 2 groups separated on the independent

variable– 1 dependent variable

• Thus: 2 groups compared on 1 score or measurement

• Several versions of t-test for use in various circumstances– Independent t (groups not related)– Correlated t (groups related or “repeated

measures”)– Unpooled variance (most samples)– Pooled variance (small samples)




The t-Test


The t -Test• t-Test examines 2 group means to see

if they are “significantly” different• The “significant” refers to statistical

significance only• Uses variance within and between

groups to compare the means (Remember, variance is related to distance of scores from the group mean)

• To have a “significant” t-value, variance between groups must be greater than variance within groups by a critical amount




t-Tests:Interpreting the “Answer”

t = value of t will be reported

df = degrees of freedom for the test will be listed




ANOVA (F test)• Must have:

– 1 or more independent variables (“Factors”)– 2 or more groups separated on the independent

variable(s)– 1 dependent variable – For more than 1 dependent variable, run series of

ANOVAs or a MANOVA• Compare to t-Test requirements• Several variations of ANOVA family, including:

– One-way ANOVA– Factorial ANOVA– MANOVA (Multiple ANOVA)– ANCOVA (Analysis of Co-Variance)

• To get a “significant” F, variance between groups must exceed variance within groups by a critical amount

• F is actually a ratio of variance between to variance within

• Within-group variance is “error” variable





One-Way ANOVA• Must have

– 1 Factor (independent variable)– 2 or more groups to compare– Groups are separated on the

identified factor– 1 dependent variable – For more than 1 dependent variable,

run series of ANOVAs or a MANOVA• One-way ANOVA with 1 Factor

and only 2 goups = t-Test– t2 = F– Can use either test– t is usual choice in this case

• 1-way ANOVA must be used for 1 Factor and more than 2 groups




1-way ANOVA:Interpreting the “Answer”

F = value of F will be reported

df = 2 degrees of freedom for the test will be listed dfwithin and dfbetween (F2,36)




Factorial ANOVA• Must have

– 2 or more Factors (independent variable)

– 2 or more groups to compare– Groups are separated on the

identified factors– 1 dependent variable – For more than 1 dependent variable,

run series of ANOVAs or a MANOVA• Each Factor may have 2 or more

variations or “levels”• Factorial ANOVA with only 2

factors are usually called “2-way ANOVAs”




Let’s look at some examples Note difference between: - Factors - Levels - Cells

Factorial ANOVA:Interpreting the “Answer”

F = multiple values of F will be reported: (a) an F for “main effect” for each Factor (b) an F for “interaction” of the factors

df = degrees of freedom for each F will be listed

p = or p < or p > = or < or > (or % level) %, probability or alpha level will be listed for each F


Post-Hoc Tests with ANOVA


• “After the fact” tests – done after ANOVA in certain conditions– When have more than 2 groups– When find significant F with more

than 2 groups

• Done to locate exactly where the significant F occurs

• 2 common tests – each used under certain circumstances– Tukey test (T-method)– Scheffe tests (S-method)



Questions and Discussion

Questions and Discussion

introduction to basic statistical tools for research oced 5443 interpreting research in oced dr....

Documents

types of data

deviation of score

sets of data

variations data

understandgood data

measures of relationship

deviation scores score

average deviation