research method about population and sample .pptx

for student in college

1. Populations and Samples Delivered by Nurfaizah

2. Populations and samples A population is: the full collection of people or things. A sample is: some subset of the population intended to represent the population. Population Sample Data obtained from all members of the population is known as a census . Advantages of sampling Cheaper/quicker than taking a census. Useful when testing of items results in their destruction (e.g. life-time of light bulb) Disadvantages of sampling Potential for bias. Natural variation between any two samples due to variation in data. Cheaper/quicker than taking a census. Useful when testing of items results in their destruction (e.g. life-time of light bulb) Potential for bias. Natural variation between any two samples due to variation in data. the full collection of people or things. some subset of the population intended to represent the population ?

3. Sampling key terms Sample ! Each individual thing in the population that can be sampled is known as a sampling unit . ! The list of all those within the population that can be sampled is known as the sampling frame .

4. Random sampling Suppose that the heights of people in a population are represented using a random variable , where is (as you might expect), normally distributed, e.g.   Bro Helping Hand : This might conceptually seem confusing as a population is a list of things. The population can be represented as a distribution where the outcomes are possible samples . For example, if a population is all possible lottery tickets, then the distribution representing it is a uniform distribution whose outcomes are all the possible tickets.     How could we represent the possible choice of 1 st member of our sample? We want a sample with things in it.   A random variable where   Bro Helping Hand : Notice we’re representing the possible choice of the item in the sample, not the item itself. must have the same distribution as , because our sample item is drawn from the population.   How could we represent the possible choice of th member of our sample?   A random variable where   ! A random variable 𝑋 1where 𝑋 1 ~𝑁 1.5, 0.3 A random variable 𝑋 𝑛where 𝑋 𝑛 ~𝑁 1.5, 0.3

5. Random sampling ! A simple random sample , of size , is one taken so that every possible sample of size has an equal chance of being selected. It consists of the observations from a population where each : Are independent random variables Have the same distribution as the population.   This means for example that if the first person chosen for our sample is Indian, that doesn’t make it any less or more likely our second choice will be Indian, i.e. our second choice is independent of the first. This will all become a lot clearer once we do an example …

6. Random sampling We might wish to calculate some numerical property of a population or a sample, e.g. mean, variance, mode, range. ! A population parameter is a quantity calculated from the population . ! A statistic is a quantity calculated (solely) from the observations in a sample . e.g. is a statistic (the average of the 2 nd , 5 th and 8 th items in the sample) is a statistic. But is not as it involves the population mean , which is not known purely from the sample.   The idea of a statistic is that the we hope it resembles the equivalent population parameter. For example, if we’re trying to find the mean age in England, we might take a sample, calculate the sample mean age , and hope this represents the ‘true’ unknown population mean age … (Recall that sample mean and population mean )  

7. Sampling Distribution of a Statistic ! The sampling distribution of a statistic gives all the values of a statistic and the probability that each would happen by chance alone. 0 1 1 0 1 1 2 0 0 0 Statistics for this sample could be the mode number of children, median , maximum , mean , …   0 0 0 1 0 2 1 0 1 1 1 2 2 0 2 1 2 2     0.5 1 0.5 1 1.5 1 1.5 2 1 2 1 1 2 2 2 2 Possible Samples? Note : Because each thing in the sample is independently drawn from the population, we technically have sampling with replacement, and hence the same item could be in the sample twice. In practice however (and in exams) you won’t have to worry about this, as the population in exams is assumed to be infinitely large.     Max 0.25 1 0.56 2 0.19 0.25 1 0.56 2 0.19 Sampling distribution for sample maximum. BOB Suppose we had 10 families which form the population of an island (The Isle of Bob), for which we know the number of children in each family. Suppose we took a (very small!) sample of 2 families. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Let’s reflect on what we did. #1 : We considered all possible samples, and the probability of each sample occurring. #2 : We’re interested in some statistic for each sample (let’s say the sample maximum) #3 : Thus we now have a distribution over possible values of the statistics across all possible samples we could have had, i.e. the ‘sampling distribution’.