No, there is not any way to compensate for the large standard errors that are associated with small samples. The only alternative is to use a higher value for your probability cut-off (e.g., .10 instead of .05).

If you can say more about your mixed methods design, we might be able to give you advice about how to integrate the quantitative and qualitative components.

No, there is not any way to compensate for the large standard errors that are associated with small samples. The only alternative is to use a higher value for your probability cut-off (e.g., .10 instead of .05).

If you can say more about your mixed methods design, we might be able to give you advice about how to integrate the quantitative and qualitative components.

The standard error is a product of two things : the sample size and the variability. Variability comes from two sources : true variability in the thing you are measuring, and variability due to measurement error.

Improving standard errors by increasing sample size is expensive. To divide the standard error by 2, you must increase the data by 4.

The alternative is to reduce measurement error by choosing high-reliability measures, by measuring under carefully controlled conditions etc. It's cheaper, often.

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EDUCATIONMATHSTATISTICSHOW SAMPLE SIZE AFFECTS THE MARGIN OF ERROR

HOW SAMPLE SIZE AFFECTS THE MARGIN OF ERROR

Statistics For Dummies, 2nd Edition

RELATED BOOK

Statistics For Dummies, 2nd Edition

By Deborah J. Rumsey

In statistics, the two most important ideas regarding sample size and margin of error are, first, sample size and margin of error have an inverse relationship; and second, after a point, increasing the sample size beyond what you already have gives you a diminished return because the increased accuracy will be negligible.

The relationship between margin of error and sample size is simple: As the sample size increases, the margin of error decreases. This relationship is called an inverse because the two move in opposite directions. If you think about it, it makes sense that the more information you have, the more accurate your results are going to be (in other words, the smaller your margin of error will get). (That assumes, of course, that the data were collected and handled properly.)

Suppose that the Gallup Organization’s latest poll sampled 1,000 people from the United States, and the results show that 520 people (52%) think the president is doing a good job, compared to 48% who don’t think so. First, assume you want a 95% level of confidence, so you find z* using the following table.

z*-Values for Selected (Percentage) Confidence

Levels

Percentage Confidence z*-Value

80 1.28

90 1.645

95 1.96

98 2.33

99 2.58

From the table, you find that z* = 1.96.

The number of Americans in the sample who said they approve of the president was found to be 520. This means that the sample proportion,

image0.png

is 520 / 1,000 = 0.52. (The sample size, n, was 1,000.) The margin of error for this polling question is calculated in the following way:

image1.png

According to this data, you conclude with 95% confidence that 52% of all Americans approve of the president, plus or minus 3.1%.

Using the same formula, you can look at how the margin of error changes dramatically for samples of different sizes. Suppose in the presidential approval poll that n was 500 instead of 1,000. Now the margin of error for 95% confidence is

image2.png

which is equivalent to 4.38%. If n is increased to 1,500, the margin of error (with the same level of confidence) becomes

image3.png

or 2.53%. Finally, when n = 2,000, the margin of error is

image4.png

or 2.19%.

Looking at these different results, you can see that larger sample sizes decrease the margin of error, but after a certain point, you have a diminished return. Each time you survey one more person, the cost of your survey increases, and going from a sample size of, say, 1,500 to a sample size of 2,000 decreases your margin of error by only 0.34% (one third of one percent!) — from 0.0253 to 0.0219. The extra cost and trouble to get that small decrease in the margin of error may not be worthwhile. Bigger isn’t always that much better!

No, is not possible. So you should appropriate sample size for your researches.