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Chapter 13
Understanding research results:
statistical inference
Inferential statistics
Are necessary to give meaning to sample
data

Population data is harder to acquire
Used to determine if we can make statements
that the results reflect what would happen if
we were to conduct the experiment
repeatedly w/ multiple samples
Allow us to arrive at conclusions on the basis
of sample data
Null and research hypotheses
Null hypothesis -- H0
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the population means are equal
The observed difference is due to random error
 The H0 is rejected when there is a very low probability that the obtained
results could be due to random error.
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The IV had no effect
Research hypothesis -- H1
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The population means are not equal
The IV had an effect on the DV
If we can determine the null hypothesis is false, we then accept
the research hypothesis is true.
Statistical significance
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A very low probability that the obtained results could be due to
random error.
Results are due to the IV’s effect on the DV
Probability and sampling
distributions
Probability
 The likelihood of the occurrence of some event or outcome
 What is the likelihood this occurrence will differ in the
population
 Based on specific information
Sampling distributions
 Based on the assumption that the null hypothesis is true
 When it is highly unlikely the null hypothesis is true (0.05 or
5% chance), the researcher rejects the H0 and accepts the H1
Sample size
 Larger sample sizes are good
 With more observations, the greater the likelihood of obtaining
an accurate estimate of the true population value
The t test
t test
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Commonly used to test if 2 groups significantly
differ from each other
Does the mean of one group significantly differ
from the mean of another group?
= group difference / within group variability
 Group difference – the difference between the obtained
means
 Within group variability – the amount of variability
around the group mean

If the t value has a low probability (a value of 0.05
or less) of occurring, the H0 is rejected
The t test
Degrees of freedom
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df
= the total # of participants in the groups – the number of groups
The number of scores free to vary once the means
are known
One tailed vs. two tailed tests

One tailed tests are used if the research hypothesis
specified the direction of difference between the
groups
 H1 = Group 1 will be > than Group 2

Two tailed tests are used if the research hypothesis
did not specify a predicted direction of difference
 H1 = Two groups will differ
The F test
F test is a.k.a. the ANOVA
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(analysis of variance)
An extension of the t test
Asks if there is a significant difference between 3 or
more groups
Used to evaluate the results of factorial designs
 Used when two or more independent variables are used

A ratio of two types of variance
 Systematic variance – the deviation of the group means from
the mean score of all individuals in all groups

Between group variance
 Error variance – the deviation of the individual scores in each
group from their respective group means
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Within group variance
The larger the F ratio, the more likely it is that the
results are significant
The F test
Calculating effect size
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Effect size – the magnitude of the effect
Can be in terms of t test or standard deviation
Provides information on the size of the relationship
between the variable studied
Confidence intervals

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A 95% confidence interval indicates that we are 95%
sure that the population value lies within the range
As the sample increases the confidence interval
narrows
 This occurs because larger sample sizes are more likely to
reflect the population mean
Type I and II errors
Correct decisions
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Rejecting the null hypothesis and the research hypothesis is true
Accept the null hypothesis and the null hypothesis is true
Type I error
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Rejecting the null hypothesis when the null hypothesis is true
False positive; false alarm
The probability of making a Type I error is deterined by the alpha
level, α
Type II errors
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Accepting the null hypothesis when the research hypothesis is true
False negative
The probability of a type II error is called β
Choosing a significance level
Researchers use a .05 or .01 significance level

Generally researchers think the consequences of making a
Type I error are more serious than a Type II error
Interpreting non-significant results

Even though significance is not reached does not mean
there is no relationship between the variables
 Statistical significance does not always mean practical
significance
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To troubleshoot, modify the dependent measure for better
reliability and sensitivity
If there are small sample sizes, it is harder to do statistical
tests
Do multiple studies to ensure reliability
Analysis
Choosing a sample size: power analysis
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Power: the probability of correctly rejecting the null
hypothesis
Power = 1 – p (Type II error)
A power between .70 and .90 is usually used
Usually done by a stats computer program
Significance of a Pearson R correlation coefficient

A statistical significance test allows you to decide whether to
reject the null hypothesis and conclude that the correlation
is greater than 0.0
 i.e. perform a t test to compare the obtained coefficient w/ the
null hypothesis correlation (0.0)
Computer analysis of data

MS Excel, SPSS, SAS, Minitab…
Selecting the appropriate
significance test
One IV – 2 groups only
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Nominal scale data
 Chi square
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Ordinal scale data
 Independent groups: Mann Whitney U
 Repeated measures or matched participants: Wilcoxon’s T or
the sign test
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Interval or ratio scale data
 Independent groups: t test
 Repeated measures or matched participants: t test or RM
ANOVA
One IV – 3 or more groups
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Nominal scale data
 Chi square
Selecting the appropriate
significance test
One IV – 3 or more groups

Ordinal scale data
 Independent groups: Kruskal – Wallace H test
 Repeated measures: Friedman T test
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Interval or ratio scale data
 1 way ANOVA
Two or more IVs
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Nominal scale data
 Chi square
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Ordinal scale data
 No appropriate test available

Interval or ratio scale data
 2 way ANOVA