Chapter 13 – Understanding Research Results: Statistical Inference

SAMPLES AND POPULATIONS

•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

INFERENTIAL STATISTICS

•Equivalence of groups is achieved by experimentally controlling all other variables or by

randomization

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

NULL AND RESEARCH HYPOTHESES

•Statistical inference begins with a statement of the null hypothesis and a research (or alternative)

hypothesis

•The null hypothesis is simply that the population means are equal—the 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 AND SAMPLING DISTRIBUTIONS

•Probability is the likelihood of the occurrence of some event or outcome

•We want to specify the probability that an event will occur if there’s no difference in population

•Probability: the case of ESP

oESP = extrasensory perception

oThe probability required for significance is called the alpha level – the 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

EXAMPLE: THE t AND f TESTS

•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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