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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 ā statistics designed to determine whether results based on sample

data are generalizable to a population.

The assumption in an experimental design is that if the groups are equivalent, any

differences in the dependent variable must be due to the effect of the independent variable.

However, it is also true that the difference between any two groups will almost never be

zero i.e. there will be some difference in the sample means, even when all of the principles

of experimental design are utilized.

The difference in the sample means reflects any true difference in the population means

(i.e. the effect of the independent variable) plus any random error. Inferential statistics give

the probability that the difference between means reflects random error rather than a real

difference.

Null hypothesis ā The hypothesis, used for statistical purposes, that the variables under

investigation are not related in the population, that any observed effect based on sample

results is due to random error. The population means are equal and the independent

variable had no effect.

Research hypothesis ā The hypothesis that the variables under investigation are related

in the population-that the observed effect based on sample data is true in the population.

The population means are not equal and the independent variable had an effect.

Null hypothesis is more precise as it suggests that the population means are exactly equal

and such precision cannot be inferred from the research hypothesis. So, the research

hypothesis is accepted by rejecting the null hypothesis.

Statistical significance ā Rejection of the null hypothesis when an outcome has a low

probability of occurrence (usually 0.5 or less) if, in fact, the null hypothesis is correct.

Probability ā The likelihood that a given event (among a specific set of events) will occur.

In statistical inference, we want to specify the probability that an event (in this case, a

difference between means in the sample) will occur if there is no difference in the

population. The question is: What is the probability of obtaining this result if only random

error is operating?

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