Chapter 13 - Detailed & Easy to Learn

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14 Dec 2010
Chapter 13 – Understanding Research Results: Statistical Inference
Inferential statistics are necessary because the results of a given study are based on data obtained
from a single sample of research participants
Inferential statistics are used to determine whether we can, in fact, make statements that the
results reflect what would happen if we were to conduct the experiment again and again with
multiple samples—in essence, we are asking whether we can infer that the difference in the
sample means reflect a true difference in the population means
Equivalence of groups is achieved by experimentally controlling all other variables or by
oThe assumption is that if they groups are equivalent, any differences in the dependent
variable must be due to the effect of the independent variable
There will always be some difference in the sample means, the difference will never be 0
oDifference in the sample means reflects any true difference in the population means plus
any random error
Statistical inference begins with a statement of the null hypothesis and a research (or alternative)
The null hypothesis is simply that the population means are equalthe observed difference is due
to random error
The research hypothesis is that the population means are, in fact, not equal
The null hypothesis states that the independent variable had no effect; the research hypothesis
states that the independent variable did have an affect (Null = H0, Research = H1)
The logic of the null hypothesis is this: if we can determine that the null hypothesis is incorrect,
then we can accept the research hypothesis as correct—meaning that the independent variable had
an affect
The null hypothesis is used because it is a very precise statement—the population means are
exactly equal—this permits us to know precisely the probability of the outcome of the study
occurring if the null hypothesis is correct
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The null hypothesis is rejected when there is a very low probability that the obtained results could
be due to random error –this is what is meant by statistical significance. A significant result is one
that has a very low probability of occurring if the population means are equal
oSignificance indicated that there is a low probability that the difference between the
obtained sample means was due to random error
Probability is the likelihood of the occurrence of some event or outcome
We want to specify the probability that an event will occur if theres no difference in population
Probability: the case of ESP
oESP = extrasensory perception
oThe probability required for significance is called the alpha levelthe most common
alpha level probability used is 0.05; the outcome of the study is considered significant
when there is a 0.05 or less probability (aka a 5 out of 100 chance) that the results were
due to random error in one sample from the population
Sampling distributions
oThe sampling distribution is based on the assumption that the null hypothesis is true
oAll statistical tests rely on sampling distributions to determine the probability that the
results are consistent with the null hypothesis
oWhen the obtained data are very unlikely according to the null hypothesis expectations,
the researcher decided to reject the null hypothesis and accept the research hypothesis
Sample size
oAs the size of your sample increases, you are more confident that your outcome is
actually different from the null hypothesis expectation
The t tests is most commonly used to examine whether 2 groups are significantly different from
each other
The F test is a more general statistical test that can be used to ask whether there is a difference
among 3 or more groups or to evaluate the results of factorial design
t Test
oIf the obtained has a low probability of occurrence (0.05 or less), then the null hypothesis
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