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Statistics
Statistics
• Types
• Methods of organizing • Descriptive
statistics
and analyzing
• Definition
quantitative data
– Central tendency,
variability, etc.
• Inferential statistics
– Chi-squares, t-tests,
F-ratios, etc.
Descriptive Statistics
• Measurement scales
–
–
–
–
Nominal (male/female, yes/no)
Ordinal (high to low)
Interval(1, 2, 3. . .)
Ratio
Visual Depictions of Data
• Frequency
distributions
• Histograms and Bar
Graphs
Visual Depictions of Data
90
80
70
60
50
40
30
20
10
0
First graders
Second graders
Third graders
1st Qtr 2nd 3rd Qtr 4th Qtr
Qtr
Measures of Central Tendency
• Mean
• Median
• Mode
Measures of Central Tendency
• Normal distribution
• Skewed distributions
A
B
C
Measures of Variability
• How spread out the distribution of scores is from
the mean of the distribution
• Range
• Standard deviation
• Percentile Rank
• Standard Scores
34.13% 34.13%
2.14% 13.59%
13.59%
2.14%
.13%
.13%
-3
-2
-1
0
+1
+2
+3
Descriptive Statistics
• Measures of relationship
– Correlation coefficient
• High (.70 or above) Moderate (.40-.60)
Low (.20)
• Pearson product moment coefficient ®
• Correlation Matrix
Correlation Matrix
Intercorrelations Among Teacher Practices
1
1 Choice
2
3
4
1.0
2 Directives 0.01
1.0
3 Coach
0.34
1.0
0.55
0.28
0.06
4 Positive -0.34
1.0
Descriptive Statistics
• Measures of relationship
– Multiple regression
• Shows the relationship of several independent
variables with a dependent variable
• Path Analysis
Application Activity?
• Your students earned the following scores on your
recent test:
• 89, 95, 78, 50, 80, 89, 76
• What scale of measurement are you using?
• What was the range?
• Compute the mean, median and mode.
• What is your distribution like?
• The Null Hypothesis
• Level of Significance
– Type I Error
– Type II Error
• Effect Size
Let’s apply this!
Application Activity
• If the null hypothesis is rejected, we can say that
the observed results proves that the theory we are
testing is true.
• The null hypothesis will be rejected if the sample
data turn out to be _____________
consistent/inconsistent with what one would
expect if it were true.
• Which level of significance offers the greater
protection against Type I errors, .05 or .01?
• Is it possible for a researcher to make both a Type
I error and a Type II error at the same time?
Application Activity
• A researcher tells the superintendent at the
local school that the new curriculum is
statistically significantly superior to the old
curriculum. What question(s) should the
superintendent ask the researcher?
• T-Test:
• Used to compare 2 means
• Analysis of Variance (ANOVA)
– One Way
– Two Way
– Repeated Measures
• Post Hoc and Planned Comparisons
– E.g., Bonferoni, Tukey, Duncan’s, etc.
One-Way ANOVA
Stimulation
Low
High
AD/HD
Two-Way ANOVA
AD/HD
Treatment 1
Treatment 2
Control
Treatment 1
Treatment 2
Interaction
ADHD
Control
Behavior
Treatment 1
Treatment 2
• Mixed Design
Group
AD/HD
Control
Repeated Factor
Schedule Puzzle 1
Puzzle 2 Puzzle 3
• Multivariate Analysis of Variance
• Analysis of Covariance (ANCOVA
Nonparametric Tests
• Frequencies, percentages, or proportions
• Chi-square test (X2)
Importance of jobs by ethnicity
Race
Minorities
Caucasian
Ignored jobs
59.1
73.1
Mentioned jobs
40.9
26.9
Chi square significance = .00787