The null hypothesis is used in inferential statistics because it is a very precise statement – the
population means are exactly equal
This precision permits us to know the probability of the outcome of the study occurring if
the null hypothesis is true in the population
Such precision is not possible with the research hypothesis, so we infer that the research
hypothesis is likely true in the population only by rejecting the null hypothesis
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 there is no
effect in the population (e.g. group means are equal)
Significance indicates that there is a low probability that the difference
between the obtained sample means (or the non-zero correlation) was
due to random error.
PROBABILITY AND SAMPLING DISTRIBUTIONS
is the likelihood of the occurrence of some event or outcome.
Probability in statistical inference is used in much the same way
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
PROBABILITY: THE CASE OF MIND READING
Ex. Friend claims to have mind reading or ESP, you decide to test by flipping coins 10 times
Goal is to determine whether answers reflect random error (guessing) or whether
something more than random error is occurring
Null hypothesis is that only random error is operating
Research hypothesis sis that the number of correct answers shows more than random or
The probability required for significance is called the
probability used is 0.05
Outcome is considered significant when there is a 0.05 or less probability of
obtaining the results if the
is actually true.
If it is very unlikely that random error is responsible for the obtained results, the
null hypothesis is rejected.
A probability distribution called Binomial distribution
Such distributions are called
null hypothesis sampling distributions
is based on the assumption that the null hypothesis is true;
in the mind reading example, the null hypothesis is that the person is only guessing and
should therefore get 50% correct.