Transcript Parametric Statistics

Types of Inferential Statistics
• Parametric Statistics: estimate the
value of a population parameter from the
characteristics of a sample
– Assumes the values in a sample are
normally distributed
– Interval/Ratio level data required
• Nonparametric Statistics:
– No assumptions about the underlying
distribution of the sample
– Used when the data do not meet the
assumption for a nonparametric test (ordinal
and nominal data)
What are We Testing Anyway?
• Parametric Statistics:
comparing the means of two or
more groups relative to the
variance within the groups
• Nonparametric Statistics:
comparing the medians or
ranks of two or more groups
• Testing the null hypothesis
• Statistical Significance:
determination that the
differences between groups
are large enough to be unlikely
to have occurred by chance
Steps in the Test of Significance
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State the null hypothesis.
State the alternative hypothesis.
Set the level of significance associated with the null
hypothesis (Type I Error).
Select the appropriate test statistic.
Compute the test statistic value.
Determine the critical value needed for rejection of the
null hypothesis for the particular statistic.
Compare the obtained value to the critical value.
Make a decision: Accept or reject the null hypothesis.
All These Tests!
How do I know which one?
• The type of statistical test you use
depends on several factors:
– Number of independent
variables
– Number of levels of the
independent variable(s)
– Number of dependent variables
– Independent vs. dependent
samples (between vs. within
groups design)
– Scale of measurement of the
dependent variable
Selecting Statistical Tests
One Independent Variable
Measurement
Scale of the
Dependent
Variable
Interval or Ratio
Two Levels
Two Independent Variables
More than 2 Levels
Factorial Designs
Two
Two
Multiple
Multiple
Independent
Independent Dependent Independent Dependent
Groups
Groups
Groups
Groups
Groups
Independent Dependent
t-test
t-test
Ordinal
MannWhitney U
Nominal
Chi-Square
Wilcoxon
One-Way
ANOVA
Repeated
Measures
ANOVA
KruskalWallis
Friedman
Chi-Square
Two -Factor
ANOVA
Chi-Square
Dependent
Groups
Two-Factor
ANOVA
Repeated
Measures
What Can We Conclude?
• Intact Groups Design (Quasi-Experiments)
– Subject Variables: conditions over which the
experimenter has no direct control
– Cannot establish cause and effect
– Can only conclude that the groups are different from one
another
• True Experiments
– Manipulated Variables: conditions that the
experimenter controls directly and to which he randomly
assigns participants
– Allows for cause and effect interpretations
The Power of a Test
• Power of a Test: the probability that one will reject
H0 when it is a false statement. The power of a
statistical analysis is represented as 1 – β.
– Reminder: β = the probability of making a Type II Error
• It is influenced by:
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–
–
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μX - μ0
n
σ
α
Effect Size Statistics
• Due to the role of N (sample size) in the formulae for
parametric statistics, a large sample size can make a
negligible difference between groups appear
significant.
• Because of this, current APA guidelines recommend
computing effect size statistics in addition to
parametric comparisons.
Uses of the Effect Size Statistic
• The effect size statistic can be used to:
– Estimate the true effect of the IV
– Compare the results of one
research project to the
results of other projects
– Estimate the power of the
statistic
– Estimate the number of
subjects one needs in a
research project to maximize
the chance of rejecting a
false hypothesis (power)