statistics definition methods of organizing and analyzing quantitative data types descriptive...
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Statistics
Statistics
• Definition• Methods of organizing
and analyzing quantitative data
• Types
• Descriptive statistics– 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
0
10
20
30
40
50
60
70
80
90
1st Qtr 2ndQtr
3rd Qtr4th Qtr
First gradersSecond gradersThird graders
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
0 +1 +2-1-2 +3-3
34.13%34.13%
13.59%13.59% 2.14%2.14%
.13%.13%
Descriptive Statistics
• Measures of relationship– Correlation coefficient
• High (.70 or above) Moderate (.40-.60) Low (.20)
• Pearson product moment coefficient ®• Correlation Matrix
Correlation MatrixIntercorrelations Among Teacher Practices
1 2 3 41 Choice 1.0
2 Directives 0.01 1.0
3 Coach 0.06 0.34 1.0
4 Positive -0.34 0.55 0.28 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
StimulationLow High
AD/HD
Two-Way ANOVA
AD/HD
Control
Treatment 1
Treatment 2
Treatment 1
Treatment 2
Interaction
Treatment 1 Treatment 2
ADHD
Control
Behavior
• Mixed Design
AD/HD
Control
Group Repeated FactorSchedule Puzzle 1 Puzzle 2 Puzzle 3
• Multivariate Analysis of Variance
• Analysis of Covariance (ANCOVA
Nonparametric Tests
• Frequencies, percentages, or proportions
• Chi-square test (X2)
Race Ignored jobs Mentioned jobsMinorities 59.1 40.9Caucasian 73.1 26.9
Chi square significance = .00787
Importance of jobs by ethnicity