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# Sampling 1231243290208505 1

## by guest7e772ec on Apr 04, 2010

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## Sampling 1231243290208505 1Presentation Transcript

• Revisiting Sampling Concepts
• Population
• A population is all the possible members of a category
• Examples:
• the heights of every male or every female
• the temperature on every day since the beginning of time
• Every person who ever has, and ever will, take a particular drug
• Sample
• A sample is some subset of a population
• Examples:
• The heights of 10 students picked at random
• The participants in a drug trial
• Researchers seek to select samples that accurately reflect the broader population from which they are drawn.
• Population Sample Sample Statistics Population Parameters Inference Samples are drawn to infer something about population
• Reasons to Sample
• Ideally a decision maker would like to consider every item in the population but;
• To Contact the whole population would be time consuming e.g. Election polls
• The cost of such study might be too high
• In many cases whole population would be consumed if every part of it was considered
• The Sample results are adequate
• Probability Vs Non Probability Sampling
• Probability Sampling
• Drawing Samples in Random manner
• Using random numbers
• Writing names on identical cards or slips and then drawing randomly
• Choosing every nth item of the population
• First dividing the population into homogeneous groups and then drawing samples randomly
• Probability Vs Non Probability Sampling
• Non Probability Sampling
• man-on-the-street interviews
• call-in surveys
• web surveys
• Types of Variables
• Qualitative
• Quantitative
• Discrete
• Continuous
• Categorical
• Numerical
• Sampling Error
• “Sampling error is simply the difference between the estimates obtained from the sample and the true population value.”
• Sampling Error = X - µ
• Where
• X = Mean of the Sample
• µ = Mean of the Population
• Validity of Sampling Process
• Sampling Distributions
• A distribution of all possible statistics calculated from all possible samples of size n drawn from a population is called a Sampling Distribution.
• Three things we want to know about any distribution?
• – Central Tendency
• – Dispersion
• – Shape
• Sampling Distribution of Means
• Suppose a population consists of three numbers 1,2 and 3
• All the possible samples of size 2 are drawn from the population
• Mean of the Pop ( µ) = (1 + 2 + 3)/3 = 2
• Variance
• Standard Deviation = 0.82
• Distribution of the Population
• Sampling distribution of means n = 2
• = µ = 0.6 3 3,3 9 2 Mean of SD 2.5 3,2 8 2 3,1 7 2.5 2,3 6 2 2,2 5 1.5 2,1 4 2 1,3 3 1.5 1,2 2 1 1,1 1 Sample Mean Sample Sample #
•
• The population’s distribution has far more variability than that of sample means
• As the sample size increases the dispersion becomes less and in the SD
0.6 < 0.8 = µ <
• The mean of the sampling distribution of ALL the sample means is equal to the true population mean.
• The standard deviation of a sampling distribution called Standard Error is calculated as
• Central Limit Theorem ……
• The variability of a sample mean decreases as the sample size increases
• If the population distribution is normal, so is the sampling distribution
• For ANY population (regardless of its shape) the distribution of sample means will approach a normal distribution as n increases
• It can be demonstrated with the help of simulation .
• Central Limit Theorem ……
• How large is a “large sample”?
• It depends upon the form of the distribution from which the samples were taken
• If the population distribution deviates greatly from normality larger samples will be needed to approximate normality .
•
• Implications of CLT
• A light bulb manufacturer claims that the life span of its light bulbs has a mean of 54 months and a standard deviation of 6 months. A consumer advocacy group tests 50 of them. Assuming the manufacturer’s claims are true, what is the probability that it finds a mean lifetime of less than 52 months?
• Implications of CLT Cont
• From the data we know that
• µ = 54 Months = 6 Months
• By Central Limit Theorem
• = µ = 54
=
• 54 o -2.35 0.0094 52
• To find ,we need to convert to z -scores:
• From the Area table = 0.4906
• Hence, the probability of this happening is 0.0094.
• We are 99.06% certain that this will not happen
• What can go wrong
• Statistics can be manipulated by taking biased samples intentionally
• Examples