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Competency: Plans data collection procedure and describes the sample size.
Slovin’s Formula
Slovin’s Formula
If you take a population sample, you must use a formula to figure out what sample size you need to take. Sometimes you know something about a population, which can help you determine sample size. For example, it’s well known that IQ scores follow a normal distribution pattern. But what about if you know nothing about your population at all?
Whereas:
n = number of sample size
N = total population
e = error margin / margin of error
Sample question: Use Slovin’s formula to find out what sample of a population of 1,000 people you need to take for a survey on their soda preferences.
Step 1: Figure out what you want your confidence level to be. For example, you might want a confidence level of 95 percent (giving you an alpha level of 0.05), or you might need better accuracy at the 98 percent confidence level (alpha level of 0.02).
Step 2. Plug your data into the formula. In this example, we’ll use a 95 percent confidence level with a population size of 1,000.
n = N / (1 + N e2) =
1,000 / (1 + 1000 * 0.05 2) = 285.714286
Step 3: Do not round your answer to a whole number (because you cannot find a .71 to be considered as a person. You need to be careful in treating and computing the sample size or a population. Be strict in determining it.)
285.714286 = 285
What is Slovin's Formula
What is Slovin's Formula
Slovins’s formula is used to calculate an appropriate sample size from a population.
About sampling
Statistics is a way of looking at a population’s behavior by taking a sample. It’s usually impossible to survey every member of a population because of money or time. For example, let’s say you wanted to know how many people in the USA were vegetarians. Think about how long it would take you to call over 300 million people; Assuming they all had phones and could speak!. The problems with entire surveying populations are why researchers survey just a fraction of the population: a sample.
The problem with taking a sample of the population is the sample size. Obviously, if you asked just one person in the population if they were vegetarian, their answer wouldn’t be representative of everyone. But would 100 people be sufficient? 1000? Ten thousand? How you figure out a big enough sample size involves applying a formula. While there are many formulas to calculate sample sizes, most of them require you to know something about the population, like the mean. But what if you knew nothing about your population? That’s where Slovin’s formula comes in.
When Slovin’s formula is used
If you have no idea about a population’s behavior, use Slovin’s formula to find the sample size. The formula (sometimes written as Sloven’s formula) was formulated by Slovin in 1960.
The error tolerance, e, can be given to you (for example, in a question). If you are a researcher, you might want to figure out your error tolerance; Just subtract your confidence level from 1. For example, if you wanted to be 98 percent confident that your data would be reflective of the entire population then:
1 – 0.98 = 0.02. e = 0.02.
What is Stratified Random Sampling?
What is Stratified Random Sampling?
Stratified random sampling is used when your population is divided into strata (characteristics like male and female or education level), and you want to include the stratum when taking your sample. The stratum may be already defined (like census data), or you might make the stratum yourself to fit the purposes of your research. Stratified random sampling is very similar to random sampling. However, these samples are more difficult to create as you must have detailed information about what categories your population falls into.
How to Perform Stratified Random Sampling?
To perform stratified random sampling, take a random sample from within each category or stratum. Let’s say you have a population divided into the following strata:
Category 1: Low socioeconomic status — 39 percent
Category 2: Middle class — 38 percent
Category 3: Upper income — 23 percent
To get the stratified random sample, you would randomly sample the categories so that your eventual sample size has 39 percent of participants taken from category 1, 38 percent from category 2, and 23 percent from category 3. What you end up with is a mini representation of your population. According to the University of California at Davis, the following steps should be taken to obtain the stratified sample:
Name the target population.
Name the categories (stratum) in the population.
Figure out what sample size you need.
List all of the cases within each stratum.
Make a decision rule to select cases (for example, you might select the items using the largest set of random numbers).
Assign a random number to each case.
Sort each case by random number.
Follow your decision rule (#5 above) to choose your participants.
How to get a Stratified Random Sample?
“Stratified” means “in layers,” so in order to get a stratified random sample, you first need to make the layers. What layers you have depends on the characteristics of your population. For example, if you are surveying U.S. residents about their plans for retirement, you might want your layers to represent different age groups. The sample size for each strata (layer) is proportional to the size of the layer:
Steps to Get the Stratified Random Sampling
Sample question: You work for a small company of 1,000 people and want to find out how they are saving for retirement. Use stratified random sampling to obtain your sample.
Step 1: Decide how you want to stratify (divide up) your population. For example, people in their twenties might have different saving strategies than people in their fifties.
Step 2: Make a table representing your strata. The following table shows age groups and how many people in the population are in that strata:
Step 3: Decide on your sample size. If you don’t know how to find a sample size, see: Sample size (how to find one). For this example, we’ll assume your sample size is 50.
Step 4: Use the stratified sample formula (Sample size of the strata = size of entire sample/population size * layer size) to calculate the proportion of people from each group:
Note that all of the individual results from the stratum add up to your sample size of 50: 8 + 11 + 12 + 10 + 9 = 50
Step 5: Perform random sampling (i.e., simple random sampling) in each stratum to select your survey participants.
That’s how to get a stratified random sample!
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