Statistics How To

Sample Size in Statistics: How to Find it


Contents:

  1. What is a Sample Size?
  2. How to Find a Sample size:

What is a “Sample Size”?

A sample size is a part of the population chosen for a survey or experiment. For example, you might take a survey of dog owner’s brand preferences. You won’t want to survey all the millions of dog owners in the country (either because it’s too expensive or time consuming), so you take a sample size. That may be several thousand owners. The sample size is a representation of all dog owner’s brand preferences. If you choose your sample wisely, it will be a good representation.

When Error can Creep in

When you only survey a small sample of the population, uncertainty creeps in to your statistics. If you can only survey a certain percentage of the true population, you can never be 100% sure that your statistics are a complete and accurate representation of the population. This uncertainty is called sampling error and is usually measured by a confidence interval. For example, you might state that your results are at a 90% confidence level. That means if you were to repeat your survey over and over, 90% of the time your would get the same results.

A census is where every member of a population is surveyed, not just a sample.

A census is where every member of a population is surveyed, not just a sample.


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How to Find a Sample Size in Statistics

Watch the video or read on below:

Links mentioned in the video:
95% CI Table
calculator.
sample size
A sample is a percentage of the total population in statistics. You can use the data from a sample to make inferences about a population as a whole. For example, the standard deviation of a sample can be used to approximate the standard deviation of a population. Finding a sample size can be one of the most challenging tasks in statistics and depends upon many factors including the size of your original population.

General Tips

Step 1: Conduct a census if you have a small population. A “small” population will depend on your budget and time constraints. For example, it may take a day to take a census of a student body at a small private university of 1,000 students but you may not have the time to survey 10,000 students at a large state university.

Step 2: Use a sample size from a similar study. Chances are, your type of study has already been undertaken by someone else. You’ll need access to academic databases to search for a study (usually your school or college will have access). A pitfall: you’ll be relying on someone else correctly calculating the sample size. Any errors they have made in their calculations will transfer over to your study.

Step 3: Use a table to find your sample size. If you have a fairly generic study, then there is probably a table for it. For example, if you have a clinical study, you may be able to use a table published in Machin et. al’s Sample Size Tables for Clinical Studies, Third Edition.

Step 4: Use a sample size calculator, like this one.

Step 5: Use a formula. There are many different formulas you can use, depending on what you know (or don’t know) about your population. If you know some parameters about your population (like a known standard deviation), you can use the techniques below. If you don’t know much about your population, use Slovin’s formula..
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How to Find a Sample Size Given a Confidence Interval and Width (unknown population standard deviation)

Part two shows you how to find a sample size for a given confidence interval and width (e.g. 95% interval, 6% wide) for an unknown population standard deviation.

Sample question: 41% of Jacksonville residents said that they had been in a hurricane. How many adults should be surveyed to estimate the true proportion of adults who have been in a hurricane, with a 95% confidence interval 6% wide?

Step 1: Using the data given in the question, figure out the following variables:

  • za/2: Divide the confidence interval by two, and look that area up in the z-table:
    .95 / 2 = 0.475
    The closest z-score for 0.475 is 1.96.
  • E (margin of error):  Divide the given width by 2.
    6% / 2
    = 0.06 / 2
    = 0.03
  • phat: use the given percentage.  41% = 0.41. If you aren’t given phat, use 50%.
  • qhat :  subtract phatfrom 1.
    1 – 0.41 = 0.59

Step 2:Multiply phatby qhat. Set this number aside for a moment.
0.41 × 0.59 =  0.2419

Step 3: Divide Za/2 by E.
1.96 / .03 = 65.3333333

Step 4: Square Step 3:
65.3333333 × 65.3333333 = 4268.44444

Step 5: Multiply Step 2 by Step 4:
0.2419 × 4268.44444 = 1,032.53671
= 1,033 people to survey.
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How to Find a Sample Size Given a Confidence Interval and Width (known population standard deviation)

Part 3 shows you how to determine the appropriate sample size for a given confidence interval and width, given that you know the population standard deviation.

Sample question: Suppose we want to know the average age of an Florida State College student, plus or minus 0.5 years. We’d like to be 99% confident about our result. From a previous study, we know that the standard deviation for the population is 2.9.

Step 1: Find z a/2 by dividing the confidence interval by two, and looking that area up in the z-table:
.99/2 = 0.495.  The closest z-score for 0.495 is 2.58.

Step 2: Multiply step 1 by the standard deviation.
2.58 * 2.9 = 7.482

Step 3: Divide Step 2 by the margin of error. Our margin of error (from the question), is 0.5.
7.482/0.5 = 14.96

Step 4: Square Step 3.
14.96 * 14.96 = 223.8016

That’s it! Like the explanation? Check out our statistics how-to book, with a how-to for every elementary statistics problem type.
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How to find a sample size in Excel.

Watch the video or read the steps below:

How to use Excel Sampling to find a Sample

If you have a set of data and you know your sample size, you can use Excel’s Data Analysis toolpak to select either a periodic sample or a random sample. A random sample is just that — randomly selected from your data set. A periodic sample (also called a systematic sample) is where Excel chooses the nth data item to include in your sample. For example, if you wanted to choose every 5th number from the following list: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, Excel would return 8 and 13 (the 5th and 10th numbers in order).

If you don’t know what sample size you need, calculate it before using the Data Analysis tool (using the methods outlined at the top of this article). The Data Analysis tool can help you extract a sample, but it can’t help you decide on the size. Why? There are many “human” factors that go into selecting a sample size including budget, prior research (you can use a sample size from previous research) and tables constructed from previous research.

How to use Excel Sampling to find a Sample: Steps

Step 1: Enter your data items into Excel. You can enter your data into rows or columns. Ensure the rows and columns are even; for example, enter data into column A to cell 12 and column B to cell 12.

Step 2: Click “Data” and then click “Data Analysis.” If you don’t see Data Analysis on your toolbar, load the Data Analysis Toolpak.

Step 3: Click “Sampling” and then click “OK.”

excel sampling.

Data entered into a worksheet for Excel sampling: the rows and columns are even.

Step 4: Click in the Input Range box and then select your entire data set.

Step 5: Click either “Periodic Sampling” or “Random Sampling.” If you choose periodic, enter the nth number (i.e. every 5) and if you choose random sampling, enter the sample size.

Step 6: Choose an output range. For example, click the “New Worksheet” button and Excel will return the sample in a new worksheet.

Step 7: Click “OK.”

That’s it!

Check out our YouTube channel for more Excel tips and help!
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Effective Sample Size..
Unequal sample size.

Sample Size in Statistics: How to Find it was last modified: November 5th, 2017 by Stephanie Glen