times, there will be something close to 5,000 cases of heads and 5,000 cases
of tails. In medicine, for every 1,000 people who take some harmful substance,
X, it may be estimated
from research that 565 will become infected
with
disease Y.
Truth
Probability can be used to describe the degree of confidence that a
proposition such as a behavioural law is true. Sometimes a behavioural law is
established by an experiment where an independent variable is manipulated
systematically, and the effect in response to this on another
so-called
dependent variable is measured. These changes may be just a “yes” or a “no,”
but they can also consist of measurable responses. In this latter case, the issue
is whether any changes to the dependent variable are due to variations between
samples or are genuine products of changes to the independent variable.
In these circumstances researchers utilise confidence intervals to determine if
results can be accepted as demonstrating the plausibility of the truth of the
causal law. Confidence intervals quantify the degree of certainty with which an
experimental outcome can be believed.
Common levels are 90%, 95%, 99%
and 99.9%. Confidence levels determine the probability that the experiment has
demonstrated the causal law to be consistent with the observed data.
Relationship of Likelihood and Frequency
Let us consider the relationship between these two forms, “how often” and
“how likely”. “How often” can predict “how likely,”
and “how likely”
can
predict “how often”.
How Likely Predicting How Often
Probability of “how likely” can be a predictor of “how often”. To illustrate, let
us return to the example of the deck of cards. The probability of drawing any
particular card (for example the Ace of Hearts) from a deck of 52 is 1/52. This
probability of 1/52 has a “physical” interpretation: it means that we would
expect, on average, to draw the Ace of Hearts once in every 52 times we
pulled a card from a shuffled pack. In fact, this interpretation gives us an easy
bridge from ‘how likely’ to ‘how often.’
Assume now that we keep on drawing one card from deck this until we have
drawn a card in this way 52 million times. At this point, utilising the law of
large numbers, we can predict that each card will have been drawn
approximately [52,000,000 x (1/52)] times, that is, 1 million times. In other
words, we now have a prediction of ‘how often’ based on ‘how likely.’
This example can be generalised to postulate that “how likely” is a good
predictor of “how often” in the long run. The point to using the long run is that
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