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[size=12]How to determine the extent to which the sample represents the population as a whole
[/size] To find out to what extent a particular sample value deviates from the population value, a range of interval around the sample value can be worked out which will most probably contain the population value.
“The range of this interval is called the confidence interval”
For example:
A 95 % confidence interval of 152 to 164 centimeter of mean height of a population of women means that you are 95 % certain that the real population mean, which you cannot know exactly unless you measure the heights of all women, lies between 152 to 164 cm (152 cm is the lowest and 164 cm is the upper confidence limit)
The calculation of a confidence interval takes into account the “STANDARD ERROR”.
The standard error gives an estimate of the degree to which the sample mean varies from population means. It is computed on the basis of standard deviation.
Now I will discuss how to calculate:
· The standard error and 95 % confidence interval of mean (for numerical data) and
· The standard error and 95 % confidence interval of percentage (for categorical data)
Standard error and 95 % confidence interval of mean
When dealing with numerical data you may wish to estimate to what degree the sample mean varies from the population mean
The standard error of mean is calculated by dividing the standard deviation by the square root of the sample size
Standard deviation /√sample size or SD/ √n
It can be assumed for normally distributed variable, that approximately 95% of all possible samples means lie within two standard errors of population mean. In other words, we can be 95% sure that the population mean , of which we want to have the best possible estimate , lies within two standard errors of our sample mean.
When describing variables statistically you usually present the calculated sample mean plus or minus two standard errors. This is then called 95%
“Confidence interval” it means that you are 95% sure that the population mean is within this limit.
Example:
The weight of randomly selected sample of 11 three years old children were taken, The sample mean was 16 kg and the standard error of deviation of sample was 2 kg
The standard error is
2√ 11=0.6 kg
the 95% confidence interval is
16 plus, minus (2x 0.6) = 14.8 to 17.2 kg
this means that we are approximately 95% certain that the mean weight of all three years old children in your population lies between 14.8 and 17.2 kg
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