Why is 30 a good sample size

If you were to go back and run the experiment again you could observe that same statistically significant difference. The statistic associated with 1 is alpha, commonly called the p-value and the statistic associated with 2 is beta. The value 1-beta is called the power and it expresses the probability that you will be able to achieve a given alpha should you repeat the same experiment with the same number of samples.

Sample size calculators allow you to specify the level of certainty you would like to have that a difference exists alpha , the degree to which you would like to be certain that you could repeat this finding 1-beta and it requires that you define the size of a difference you want to detect given your prior definition of alpha and beta.

The two most common ways of defining a difference is by defining population means and standard deviations or changes in observed percents. Given the degree of precision of many measurement instruments it is quite easy to get statistically significant results of no consequence.

In this situation what your analysis has told you is your measurement system is really good at detecting differences. In these cases the existing data will be presented along with a request for increased funding to check out the possibility of the existence of something of medical value.

Butler, Thank you very much for your detailed explanations. I greatly appreciate the time and effort you made to articulate your responses. In my line of work, my company does bill review for other companies. Say, in a 6-month period, we processed 10, bills. Clearly, we cannot audit all 10, Am I to understand from your previous comment that instead of auditing , I could audit 2 and the results of those 2 would be sufficient for me to make inferences about the 10, in the population?

The problem is the question you are asking in your second post is not the same question you asked in your first post. In your first post you essentially asked: how many samples do I need in order to make inferences about a population? The answer, as I stated is a minimum of 2. Example 1: The view from the perspective of Means and Standard Deviations.

I have two populations. From the first population my measurements for a particular property are 2 and 3. From the second population my measurements for the same property are 8 and Population 1: Mean The mean is the average data point value within a data set. Example 2: The view from the perspective of percentages of defects: Again I have two populations and for each of the two populations I take two samples and determine if the samples are defective or not.

For population 1 I have 2 successes and 0 defects. For population 2 I have 0 successes and 2 defects. I have a measure of the proportions defective for the two populations and, with the sample size I have I cannot say there is any difference in these proportions. The question you are asking in your second post is not about drawing inferences about a population rather it is about drawing inferences about the detectable difference between measures of two populations predicated on characteristics of those populations.

That question takes you into the realm of my second post to this thread. Now the question is: What kind of a sample, comprised of successes and failures, must I draw in order to have a specified degree of probability that the sample represents a given level of failure that differs from a null proportion by some amount.

So the short answer is that the approach you have taken is correct and in that case you will need a sample of The way I read what you have told your program is that you have a null proportion defective of.

My apologies for not being clear previously. She approached me and said that based on some data she received, she believes there is an issue with bills my company is processing; namely, that bills are being processed incorrectly, which is causing rework for us and our customers. I asked her what the magnitude of the problem is. In other words, we process literally millions of bills annually.

So, I suggested we estimate the proportion of bills that are defective out of the total population of bills we process annually. Since we cannot audit the millions of bills we process annually, we could pull a sample, and based on the proportion of those bills that are defective in the sample, we could create a confidence interval for the population proportion.

I used the Excel spreadsheet attached to calculate this. Most statisticians agree that the minimum sample size to get any kind of meaningful result is If your population is less than then you really need to survey all of them.

This exceeds , so in this case the maximum would be Even in a population of ,, sampling people will normally give a fairly accurate result. Suppose that you want to survey students at a school which has pupils enrolled. The minimum sample would be This would give you a rough, but still useful, idea about their opinions. The maximum sample would be , which would give you a fairly accurate idea about their opinions. In practice most people normally want the results to be as accurate as possible, so the limiting factor is usually time and money.

In the example above, if you had the time and money to survey all students then that will give you a fairly accurate result. In that case you can use the following table. Simply choose the column that most closely matches your population size. You will see on this table that the smallest samples are still around , and the biggest sample for a population of more than is still around Does sample size affect t-test? Which t test should I use? Is 15 a good sample size?

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