PROBABILITY

Relationships between samples and populations are often described in terms of probability.

The goal of inferential statistics is to use the limited information from samples to draw general conclusions about populations.

The relationship between samples and populations is usually defined in terms of probability.

The reasoning of statistical inference rests on asking

“ How often would this method give a correct answer if I used it very many times?”
or

“What would happen if we did this many times?”

CHANCE BEHAVIOR IS UNPREDICTABLE IN THE SHORT RUN BUT HAS A REGULAR AND PREDICTABLE PATTERN IN THE LONG RUN

The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions.

Two interpretations:

1.        Long-run relative-frequency interpretation

Probability is the long run, expected frequency of a particular outcome

Outcome: result of an experiment or event.

Frequency: how many times something occurs (f)

Relative frequency: number of times something occurs relative to the number of times it could have occurred. (f/N)

Long run relative frequency: what you would expect to get in the long run, if you were to repeat the experiment many times.

2.        Subjective interpretation

Probability is how certain one is that a particular outcome will occur.

Computing probability

p = f / N      equivalent to relative frequency or proportion, because it can be expressed as either a decimal number or a percentage.

            number of possible successful outcomes

p =    ________________________________

         number of all possible outcomes