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Researchers Corner
Confidence Level and Confidence Interval
A novice researcher is often confused with terms like confidence
level and confidence interval if not
already exposed to the background. Further, there are terms like
significance level, p-value, -value,
margin of error and so on found in research papers as well as
while sampling and testing of data. Two
concepts very fundamental to all these are precision and
reliability of statistical predictions.
In day-to-day life, we encounter plenty of predictions and guess
works by all sorts of people ranging from
professional astrologers to renowned futurologists. For example,
who will win an election or a cricket
match, whether it will rain or not on a particular day, etc. are
quite common. Are these predictions
scientifically based? Do they have enough precision and
reliability to confidently accept and act? How to
judge their precision and significance? etc., are some natural
questions any rationally thinking person
would ask. Let us look from a lay-mans angle what these two
attributes of predictions, namely precision
and reliability mean and try to understand them with the simple
example. Suppose a teacher asks four of
his students to predict how much marks (out of 100) they would
score in the foregone examination before
the results are announced and their predictions
are shown in the table. Column 2 of the table
records prediction of each student. Students are
also asked to judge the chance of prediction
becoming true and the same in percentage is
shown in column 4.
All predictions in the table except that of student
`A falls in a range of marks. It is quite natural
that the chances of prediction becoming true
will increase with the increase in the range of prediction. On
the other hand, a binary prediction like true/
false or pass/ fail as well as the pin-pointed prediction like
that of student `A certainly will have lower
chances of coming true than predictions leading to a range. The
prediction of student B is very liberal in
the sense he may score marks ranging from 0 to 89 and hence
chances of this happening is as high as
99.9 percent. The prediction of student `C is challenging as he
sets lower limit of not less than 70 marks
and the chances of becoming true is reasonably high (95%).
Lastly, the prediction of student `D is very
reasonable in terms of range and the chances of becoming true
are very high. Thus predictions of `C
and `D are quite meaningful in terms of precise range of
prediction coupled with high chances of
occurring.
The range within which the expected/ predicted value falls is
called the precisionof prediction and the
chances of predicted value falling in the range is called the
reliability of prediction. The reliability is
Student Predicted
marks
Range of
Prediction
The chances (in %)
that the prediction
comes true
1 2 3 4
A 75 0 50.0
B 70 71 - 100 95
D 705 65 - 75 98
Volume 3 Issue 10 October 2011
8/3/2019 Confidence Level and Confidence Interval
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expressed as confidence leveland theconverse of it
issignificance level. That is, if the confidence
level is 98%, the significance level is 2%. The confidence level
tells how sure we can be and it is
expressed as a percentage and represents how often the
prediction lies within the confidence interval
(i.e., range). So any prediction should balance between the
precision and confidence level. For example,
a very precise prediction like that of student `A, with low
confidence level as well as very poor precision
and high confidence level like that of student `B are of less
useful in practical situation.
This is what the theory of sampling distribution reveals and the
range within which the results fall is the
confidence intervaland what falls outside ismargin of error.
However, by repeated sampling and/ or
increasing the sample size margin of error can be decreased (or
precision can be increased). In practice
there is no need for a researcher to repeatedly take samples to
arrive at desired confidence intervalor
margin of erroras there are standard tables and even websites to
get confidence interval ormargin of
error. Hence the wider the confidence intervalwe are willing to
accept, the more certain we can be that
the whole population answers would be within that range. The
confidence interval and the margin of
error tell us the amount of error that we can tolerate. Lower
margin of error (or higher confidence level)
requires a larger sample size. On the other hand, the confidence
level is the amount of uncertainty wecan tolerate.
We will see in future issues, the relation between sampling and
precision as well as how to determine
confidence interval or margin of error and sample size.
M S [email protected]
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