Download Experimental design and statistics notes

Experimental Design and
Statistics
Scientific Method
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Hypothesis building
• Null hypothesis (H0) presumes
_______________ between the D.V. and I.V.
– The null hypothesis is always assumed
_____________ until data show otherwise.
– If the data fail to support the null hypothesis the
null hypothesis is _________________.
• Alternative hypothesis (H1) presumes that the
null hypothesis is ______________.
– If data fail to support the null hypothesis, the
alternative hypothesis has been ____________.
Probability
• Statistical tests report the probability that the
results of the study are due to chance, reported
as a ______________.
• The acceptable probability of results being due
to chance is known as .
•  is often set at ____%, meaning that p = _____
is an acceptable risk of the results being due to
chance.
• Therefore, if p < ________, we will:
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• ( may also be commonly set at ____%.)
Rejection Errors
• Type I error – _____________ a null hypothesis
that is ___________.
– This incorrectly supports the prediction. (False
positive)
– Occurs when  is too liberal.
• Type II error – _____________ a null hypothesis
that is __________.
– This incorrectly rejects the prediction. (False
negative)
– Occurs when  is too restrictive.
Experimental Method
• Variable – any characteristic that can
change over time or across situations.
• Independent variable – the variable that is
• Dependent variable – the variable that is
Experimental design
• Between-groups design (independent group design)
– Each group represents a ___________________
– Only the _________ varies between each group.
– Requires __________________ of subjects to
each group to assure similarity of groups at the
beginning of the experiment.
– Used when:
Experimental design
• Within-subjects design (dependent group design)
– Each subject is exposed to ______________
• Subjects serve as _____________.
– Requires:
– ____________ powerful than independent
group design, because:
Experimental design
• Complex design
– Two or more independent variables are
studied simultaneously.
Normal distribution
• Normal frequency distribution is shown as:
• A large sample (30+) usually provides a
normal distribution.
• Skewness and kurtosis (provided by Excel)
can be used to check for normality in a small
sample. If these scores are within
__________, parametric statistical tests may
be used.
Statistical tests –
Single sample design
• Single sample z-test
– 1 sample group
– Experiment meets the following assumptions:
•
•
•
•
Data are interval or ratio
Data are normally distributed
Population mean is known
Population standard deviation is known
Statistical tests –
Single sample design
• Single sample t-test
– 1 sample group
– Experiment meets the following assumptions:
• Data are interval or ratio
• Data are normally distributed
• Population mean is known
Statistical tests –
Independent groups design
• Independent t-test
– 2 groups (different groups; each exposed to a
single condition of the I.V.)
– Experiment meets the following assumptions:
• Data are interval or ratio
• Data are normally distributed
• Variances are equal between groups (a.k.a.
Homogeneity of variance).
Statistical tests –
Independent groups design
• Mann-Whitney U test
– 2 groups
– Experiment breaks one of the following
assumptions:
• Data are interval or ratio
• Data are normally distributed
• Variances are equal between groups (a.k.a.
Homogeneity of variance).
Statistical tests –
Independent groups design
• Analysis of Variance (ANOVA) test
– 3 or more groups
– Experiment meets the following assumptions:
• Data are interval or ratio
• Data are normally distributed
• Variances are equal between groups (a.k.a.
Homogeneity of variance).
Statistical tests –
Independent groups design
• Kruskal-Wallis test
– 3 or more groups
– Experiment breaks one of the following
assumptions:
• Data are interval or ratio
• Data are normally distributed
• Variances are equal between groups (a.k.a.
Homogeneity of variance).
Statistical tests –
Dependent groups design
• Paired (correlated) t-test
– 2 groups (same subjects; each exposed to 2
different conditions of the I.V.)
– Experiment meets the following assumptions:
• Data are interval or ratio
• Data are normally distributed
Statistical tests –
Dependent groups design
• Wilcoxon test
– 2 groups
– Experiment breaks one of the following
assumptions:
• Data are interval or ratio
• Data are normally distributed
Parametric vs. Nonparametric tests
• Parametric tests are
most powerful.
• Require normal
distribution and
interval or ratio data.
• Includes:
– Independent t-tests
– Dependent t-tests
– ANOVA
• Nonparametric tests are
less powerful.
• Used when assumptions
are extremely violated or
with nominal or ordinal
data.
• Includes:
– Mann-Whitney U
– Wilcoxon
– Kruskal-Wallis
Parametric vs. Nonparametric tests
• Fundamental rule for choosing tests:
Choose the most powerful test possible!