Creating Confidence Intervals using Excel 2010 11/17/2013 V0d

www.StatLit.org/pdf/Create-Confidence-Intervals-Excel2010-6up.pdf 1

Create Confidence Intervals using Excel 2010 1

byMilo Schield

Member: International Statistical Institute

US Rep: International Statistical Literacy Project

Director, W. M. Keck Statistical Literacy Project

Slides at: www.StatLit.org/pdf

/Create-Confidence-Intervals-Excel2010-6up.pdf

Create Confidence Intervals Using Excel 2010

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Using Excel to Build One-group Margin of Error

For one-group confidence intervals:

11. Use Excel toolpak Descriptive-Statistics summary. This is simplest, but it does not automatically update if data changes.

12. Use CONFIDENCE function. It automates the Z or T inverse.

13. Use Excel basic statistical functions: average, standard deviation, sample size, and Z or T inverse.

Create Confidence Intervals using Excel 2010

You must enter a confidence level (95) to get the margin of error (Confidence).

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11a Margin of Error using Descriptive Statistics

.From Tools tool-bar, select Data Analysis at far right.

Select Descriptive Statistics.

Start here:

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11b Margin of Error using Descriptive Statistics

Confidence Level: 95% Margin of Error =T*StdDev()/Sqrt(n)

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12a. Margin of error using Confidence Functions

CONFIDENCE.NORM: Pop. Stdev known; Z-scores

CONFIDENCE.T: Pop. std dev. unknown; T-scores

All CONFIDENCE functions return a margin of errorand have three arguments: alpha, SD and sample size=Confidence.Norm (alpha, Pop. std. deviation, sample size)

=Confidence.t (alpha, Sample std. deviation, sample size)

=Confidence (alpha, Pop. Std. deviation, sample size)If CL=95%, = .05. Confidence.T = (T/Z)*Confidence.Norm

Use Confidence.Norm for proportions. Confidence is Confidence.Norm in Excel 2003.

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12b. ME using CONFIDENCE for Measurements

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Creating Confidence Intervals using Excel 2010 11/17/2013 V0d

www.StatLit.org/pdf/Create-Confidence-Intervals-Excel2010-6up.pdf 2

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12c. ME using CONFIDENCE for Proportions

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13a. Margin of Error using Excel components

Margin of Error • = Z*StdDevP(data)/Sqrt(n) = Z*Sqrt(p(1-p)/n)• = T*StdDev(data) / Sqrt(n)

Use Z if population standard deviation is known: • Z = NormSInv(0.5+CL/2)

Use T if only the sample standard deviation is known:

• T = TINV(, n-1) where = (1-CL)/2

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13b. Margin of Error using Excel components

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Using Excel to Build Two-group Margin of Error

For two-group confidence intervals of stacked data (one subject per row) without pre-sorting:

21. Use pivot tables, descriptive statistics and Z or T inverse

22. Use array IF function along with basic statistical functions: average, standard deviation, sample size and Z or T inverse

23. Use array IF function along with CONFIDENCE and other basic statistical functions

If stacked data is pre-sorted into contiguous groups, use one-group approaches

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Unsorted left; sorted rightSort makes contiguous ranges

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21. Build Margin of Error using Pivot Table Statistics

Creating Confidence Intervals using Excel 2010 11/17/2013 V0d

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22a. Build ME for Averagesfrom AverageIF and Stdev(IF)

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22b. Build ME for Proportionsfrom AverageIF and Stdev(IF)

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23a. Build ME for Averages using CONFIDENCE

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23b. Build ME for ProportionsUsing CONFIDENCE

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Survey 95% Margin of Error

Surveys typically give the size of the 95% margin of error. E.g., ± 3 percentage points.

This is the most conservative 95% margin of error for the entire survey. It is computed for =50% so it is the broadest for that sample size.

A 25% subset of the group will have a 95% margin of error that is twice as big – all other things being equal.

A question for the whole group having p ~ 1/16 will have a 95% margin of error that is half the size of the survey margin of error calculated for =50%.

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Statistical Significance and Confidence Intervals

If two 95% confidence intervals do not overlap, then the difference in means is statistically-significant. But the converse may be false: those cases that overlap may still have differences that are statistically significant.

If the 95% confidence interval for one group does not overlap the mean for the second, then the difference in means is statistically-significant – at the 0.05 level. In this case, the converse is also true: those cases where the confidence interval overlaps the mean are not statistically significant. See Conrad Carlberg’s article: www.quepublishing.com/articles/article.aspx?p=1717265&seqNum=3

Creating Confidence Intervals using Excel 2010 11/17/2013 V0d

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Statistical Significance and Confidence Intervals

Instead of looking for non-overlapping confidence intervals from two independent samples, the traditional approach is to calculate the confidence interval on the difference between the two sample means.

If that 95% interval does not include zero, then the difference is reported as being statistically significant.

If that 95% interval does include zero, then the difference is reported as being statistically insignificant.

Create Confidence Intervals using Excel 2010

You must enter a confidence level (95) to get a the margin of error (Confidence).

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11a Descriptive Statistics(with Confidence)

. From Tools tool-bar, select Data Analysis at far right.

Select Descriptive Statistics.

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Confidence Interval Overlap and Statistical Significance

Generating two-group 95% confidence intervals and looking for the presence or absence of overlap is a useful first-step in determining if the difference in sample means is statistically-significant.

The lack of overlap is generally sufficient to infer the difference is statistically-significant. The converse is not true: overlapping 95% confidence intervals may still be statistically-significant.