Transcript How to calculate Confidence Intervals and Weighting Factors

How to calculate
Confidence Intervals and
Weighting Factors
Christina Blakey
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Useful definitions
• Weighting Factors make the achieved
sample match the population
• Grossing Factors make the sample the
size of the population
• Confidence Intervals show how accurate
our estimates are
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Weighting Factors
For example, we have an unequal
number of male and female
respondents in our sample (e.g. 70%
female and 30% male) but we know
that the population is 50% female and
50% male.
In order to ensure that our results
represent the population each “male”
answer would be given more weight
than each “female” answer.
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How do we calculate Weighting
Factors?
Achieved Sample
Known Population
Weighting Factor
Men
150 (36%)
4500 (45%)
45/36 = 1.25
Women
270 (64%)
5400 (55%)
55/64 = 0.86
Total
420
9,900
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Grossing Factors
Otherwise known as population based weighting, grossing up weights
Form of weighting used to “gross up” results to the
population being studied so we can make
statements about the population rather than just
the sample
The grossing factor is the known population divided
by the achieved sample size
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Grossing Factors
Achieved Sample
Known Population
Men
150
4500
Women
270
5400
Total
420
9,900
Grossing Factor
9,900/420 = 23.6
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Combining Weighting and Grossing
Factors
Usually weighting and grossing factors are
used together
How do we combine them?
There are two ways
Both methods achieve the same result so
we will only focus on one
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Weighting and Grossing Factors
Achieved Sample
Known Population
Weighting and
Grossing Factor
Men
150
4500
4,500/150 = 30
Women
270
5400
5,400/270 = 20
Total
420
9,900
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How to apply weights in practice?
How do we add this information to our data set?
There are a number of different statistical packages
available and each have different methods of adding
weights to the data.
The simplest way is too add a column to your data set
entitled weight.
Each individual response can then be multiplied by this
column.
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Confidence Intervals (CI’s)
• Confidence intervals are one of the most
important ways that statisticians quantify the
error in an estimate
• They show how accurate our results are.
• The narrower the intervals the more accurate
our estimates are.
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Calculating Confidence Intervals
So using our example from before
Our weighted result shows that 70% of people prefer dogs to cats.
How do we calculate a 95% Confidence Interval?
A 95% confidence interval is 1.96 multiplied by the
standard error
There are different ways to calculate Standard Error for
Means and Proportions
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Calculating Confidence Intervals
The standard error for proportions is:
s.e = √ ((p (100-p)) / n)
(Where p is our result and n is our sample size)
So:
√ (( 70(100 – 70)) / 420)
√ ((70 * 31) /420)
√ (2100/420)
√5
s.e = 2.24
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Calculating Confidence Intervals
CI = 2.24 * 1.96
CI = 4.4
70 – 4.4 = 65.6
70 + 4.4 = 74.4
Therefore we are 95% confident that the true
percentage of people who prefer dogs to cats is
between 65.6% and 74.4%
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Variance, standard deviation and
standard error
Variance = the sum of
squared differences
from the mean
divided by n-1
Variance = 30 / 4 = 7.5
Standard error = the
square root of the
variance divided by
the sample size
SE = √ (variance / n)
= √ (7.5 / 5)
= 1.22
Sample
values (n=5)
Difference from
mean
Squared difference
from the mean
172
171 - 172 = -1
-1 x -1 = 1
169
2
4
168
3
9
175
-4
16
171
0
0
Mean = 171
Sum = 0
Sum of squares =1430
Confidence Intervals
So 1.96 times the standard error gives us the 95% confidence limits.
Our standard error is 1.22.
1.96 x 1.22 = 2.4
Our sample mean is 171.0
171.0 – 2.4 = 168.6
171.0 + 2.4 = 173.4
We can be 95% confident that the true mean (the population mean) lies
between 168.6 and 173.4.
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Confidence Interval Calculator
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Any questions??
• [email protected]
• 0300 24 46792
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