Download Probability Values

Lecture 9-I
Data Analysis: Bivariate Analysis and
Hypothesis Testing
Research Methods and Statistics
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Quantitative Data Analysis
• Descriptive statistics: the use of statistics to summarize,
describe or explain the essential characteristics of a data set.
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Frequency Distributions
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Measures of Central Tendency
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Measures of Variability
• Inferential statistics: the use of statistics to make
generalizations or inferences about the characteristics of a
population using data from a sample.
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Estimation
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Hypothesis Testing
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Standard Normal Distribution
≈ 99% of values fall within 3 standard deviations
≈95% of values fall within 2 standard deviations
≈68% of values fall within
1 standard deviation
-3SD
-2SD
-1SD
Mean
Mode
Median
1SD
2SD
3SD
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Standard Deviation and a Normal
Distribution
• A standard normal distribution
50% of the values fall above the mean, 50% fall below.
The mean, median and mode are the same value.
A fixed proportion of the observations lie between the
mean and any other point.
Most values are near the mean, and the farther from the
mean the value is, the fewer the number of individuals
who attained that value
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Confidence Interval
• A confidence interval is a range around a measurement that
conveys how precise the measurement is.
• “The latest ABC News-Washington Post poll showed 39
percent would vote for Dole. The ABC News-Washington Post
telephone poll of 1,014 adults was conducted March 8-10 and
had a margin of error of plus or minus 3.5 percentage points
(95 confidence interval).”
• Interpretation: a 95 percent chance that between 35.5 percent
and 42.5 percent of voters would vote for Bob Dole (39
percent plus or minus 3.5 percent).
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Confidence Interval and Level
• The confidence level tells you about how stable the estimate is.
• A larger standard deviation means a wider confidence interval.
• As confidence intervals are wider, the estimated value is
unstable and vice versa.
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Inferential Statistics: Hypothesis Testing
•
Inferential statistics is used to determine the probability that
relationships or differences are found in data from a sample
are also true in the population.
•
Null hypothesis (H0)
- There is no relationship/difference between two or more
variables in the population
•
Alternate hypothesis (H1)
- There is a relationship/difference between two or more
variables in the population
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Inferential Statistics: Hypothesis Testing
Type I and Type II Errors
Your decision based
on your sample data
The real situation in the population
H0 is true
H1 is true
Accept H0
No Error
Type II Error
Reject H0
Type I Error
No Error
•
Statistical significance testing essentially determines how
large the chance is that a researcher is committing a Type I
error.
•
This chance is given by the level of significance known as
the probability value (or p value).
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Probability Values and Effect Sizes
• Probability values indicate the significance level of a
relationship.
Probability Values
1) p values range between 0 and 1
2) The standard cut-off points for p values is .05
3) If p<.05 then the finding is statistically significant.
4) Statistical significance does not mean importance.
5) Statistical significance does not indicate the strength of the
relationship between variables.
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Probability Values and Effect Sizes
• Effect sizes indicate the strength of a relationship
Effect Size
1) Indicates the strength of a relationship between variables
0 = no relationship; 1 = perfect positive relationship
2) General effect size interpretations
+/- 0.2 = small; +/- 0.5 = moderate; +/- 0.8 = strong
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