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Introduction to Basic Statistical Tools for Research
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
Descriptive Statistics
(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
Descriptive Statistics
(Non-Inferential)
Summary Snapshot of
Sample
Descriptive Statistics
(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
Descriptive Statistics
(Non-Inferential)
Summary Snapshot of
Sample
Descriptive Statistics
(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)
Descriptive Statistics
(Non-Inferential)
Summary Snapshot of
Sample
Descriptive Statistics
(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!
Descriptive Statistics
(Non-Inferential)
Summary Snapshot of
POPULATION
Descriptive Statistics
(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
Inferential Statistics
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
• Tests of significance
• Hypothesis testing
• Infer from sample to population
Inferential Statistics
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
• Tests of significance
• Hypothesis testing
• Infer from sample to population
Inferential Statistics
• 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)
• Tests of significance
• Hypothesis testing
• Infer from sample to population
The t-Test
Inferential Statistics
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
• Tests of significance
• Hypothesis testing
• Infer from sample to population
t-Tests:Interpreting the “Answer”
t = value of t will be reported
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
Inferential Statistics
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
• Tests of significance
• Hypothesis testing
• Infer from sample to population
Inferential Statistics
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
• Tests of significance
• Hypothesis testing
• Infer from sample to population
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)
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
Inferential Statistics
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”
• Tests of significance
• Hypothesis testing
• Infer from sample to population
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
Interpretation? Let’s look at example and see what this all means
Post-Hoc Tests with ANOVA
Interpretation? Let’s look at example and see what this all means
• “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)
Introduction to Basic Statistical Tools for Research
Introduction to Basic Statistical Tools for Research
Questions and Discussion
Questions and Discussion