DIFFERENCE OF MEANS CONFIDENCE INTERVAL

DIFFERENCE OF MEANS CONFIDENCE INTERVAL

Analysis Command

Generates a confidence interval for the difference between two means.

The confidence interval for the difference between tow means is defined by:
\( (\bar{Y}_{1} - \bar{Y}_{2}) \pm \sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}} t_{1-\alpha/2,df} \)

where

\( \bar{Y}_1 \) = mean of first sample
\( \bar{Y}_2 \) = mean of second sample
s₁ = standard deviation of sample 1
s₂ = standard deviation of sample 2
\( \alpha \) = the desired significance level
df = the degrees of freedom

      = \( \frac{(\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}})^2} {(\frac{s_{1}^{2}}{n_{1}})^{2}(n_1 - 1) + (\frac{s_{2}^{2}}{n_{2}})^{2}(n_2 - 1)} \)

DIFFERENCE OF MEANS CONFIDENCE INTERVAL <y1> <y2>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable,
            <y2> is the second response variable,
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

DIFFERENCE OF MEANS CONFIDENCE INTERVAL Y1 Y2
DIFFERENCE OF MEANS CONFIDENCE INTERVAL Y1 Y2 SUBSET TAG > 2
DIFFERENCE OF MEANS CONFIDENCE INTERVAL Y1 Y2 SUBSET Y1 > 0

A table of confidence intervals is printed for alpha levels of 50.0, 75.0, 90.0, 95.0, 99.0, 99.9, 99.99, and 99.999. The sample sizes, sample means, sample standard deviations, and the standard error are also printed. The t-value and t-value X standard error are printed in the table.

None

None

CONFIDENCE LIMITS	= Generate a confidence interval for the mean.
T-TEST	= Perform a two sample t-test.
BIHISTOGRAM	= Generate a bihistogram.
QUANTILE-QUANTILE PLOT	= Generate a quantile-quantile plot.
KOLMOGOROV-SMIRNOV TWO SAMPLE TEST	= Generate a Kolmogorov- Smirnov two sample test.

Confidence intervals for the difference of two means are covered in most introductory statistics books.

Confirmatory Data Analysis

1999/03

SKIP 25
READ AUTO83B.DAT Y1 Y2
RETAIN Y2 SUBSET Y2 >= 0
SET WRITE DECIMALS 5
DIFFERENCE OF MEANS CONFIDENCE INTERVAL Y1 Y2
    

Dataplot generates the following output:

 
            Confidence Limits for the Difference Between Means
                               (Two-Sided)
 
Response Variable 1: Y1
Response Variable 2: Y2
 
 
Summary Statistics for Variable 1:
Number of Observations:                  249
Sample Mean:                             20.1446
Sample Standard Deviation:               6.4147
 
Summary Statistics for Variable 2:
Number of Observations:                  79
Sample Mean:                             30.4810
Sample Standard Deviation:               6.1077
 
Difference Between Sample Means:         -10.3364
Standard Error:                          0.7984
 
 
 
-----------------------------------------------------------------
  Confidence       t      t-Value X          Lower          Upper
   Value (%)   Value         StdErr          Limit          Limit
-----------------------------------------------------------------
      50.000   0.676         0.5400       -10.8764        -9.7965
      75.000   1.155         0.9224       -11.2588        -9.4141
      90.000   1.656         1.3222       -11.6586        -9.0142
      95.000   1.977         1.5788       -11.9152        -8.7576
      99.000   2.612         2.0856       -12.4220        -8.2508
      99.900   3.363         2.6850       -13.0215        -7.6514
      99.990   4.008         3.2002       -13.5366        -7.1362
      99.999   4.588         3.6632       -13.9996        -6.6733