Paired Means Difference Calculator

May 2024 · 3 minute read
Paired Means Difference Calculator MathCelebrity logo Image to Crop From the 2 number sets that you entered, calculate a 90% confidence interval for the difference of data d

Calculate the difference of means by subtracting each respective element from both data sets

x01 - x02 = 312 - 300 = 12
x11 - x12 = 242 - 201 = 41
x21 - x22 = 340 - 232 = 108
x31 - x32 = 388 - 312 = 76
x41 - x42 = 296 - 220 = 76
x51 - x52 = 254 - 256 = -2
x61 - x62 = 391 - 328 = 63
x71 - x72 = 402 - 330 = 72
x81 - x82 = 290 - 231 = 59

We then add our of our differences of mean and divide by the number of items in the data set:

d  =  Σx1i - x2i
  n

d  =  12 + 41 + 108 + 76 + 76 + -2 + 63 + 72 + 59
  9

d  =  505
  9

d = 56.1111

Calculate the sample variance s2 by adding the sum of squared differences from the mean:

d = (12 - 56.1111)2 = -44.11112 = 1945.7891
d = (41 - 56.1111)2 = -15.11112 = 228.3453
d = (108 - 56.1111)2 = 51.88892 = 2692.4579
d = (76 - 56.1111)2 = 19.88892 = 395.5683
d = (76 - 56.1111)2 = 19.88892 = 395.5683
d = (-2 - 56.1111)2 = -58.11112 = 3376.8999
d = (63 - 56.1111)2 = 6.88892 = 47.4569
d = (72 - 56.1111)2 = 15.88892 = 252.4571
d = (59 - 56.1111)2 = 2.88892 = 8.3457
s2  =  Sum of Squared Differences
  n - 1

s2  =  1945.7891 + 228.3453 + 2692.4579 + 395.5683 + 395.5683 + 3376.8999 + 47.4569 + 252.4571 + 8.3457
  8

s2  =  9342.8885
  8

s2 = 1167.8610625

Now calculate the sample standard deviation s:

s = √s2
s = √1167.8610625
s = 34.17398224527

- tscoreα/2 x sd/√n < d < + tscoreα/2 x sd√n

First find degrees of freedom:
Degrees of Freedom = n - 1
Degrees of Freedom = 9 - 1
Degrees of Freedom = 8

Calculate α:
α = 1 - Confidence%
α = 1 - 0.9
α = 0.1

Find α spread range:
α = ½(α)
α = ½(0.1)
α = 0.05

Find t-score for α0.05 using 8 degrees of freedom:
tscore0.05 = 2.306 <--- Value can be found on Excel using =TINV(0.1,8)

Calculate high end confidence interval total:
High End = d + tscoreα x sd/√n
High End = 56.1111 + 2.306 x 34.17398224527/√9
High End = 56.1111 + 2.306 x 34.17398224527/3
High End = 56.1111 + 26.268401019197
High End = 82.3795

Calculate low end confidence interval total:
Low End = d - tscoreα x sd√n
Low End = 56.1111 - 2.306 x 34.17398224527/√9
Low End = 56.1111 - 2.306 x 34.17398224527/3
Low End = 56.1111 + 26.268401019197
Low End = 29.8427

Now we have everything, display our 90% confidence interval:

29.8427 < d < 82.3795

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What this means is if we repeated experiments, the proportion of such intervals that contain d would be 90%

What is the Answer?

29.8427 < d < 82.3795

How does the Paired Means Difference Calculator work?

Free Paired Means Difference Calculator - Calculates an estimation of confidence interval for a small or large sample difference of data. Confidence interval for paired means
This calculator has 1 input.

What 3 formulas are used for the Paired Means Difference Calculator?

Degrees of Freedom = n - 1
α = 1 - Confidence%
σ12/n1 + σ22/n2

For more math formulas, check out our Formula Dossier

What 3 concepts are covered in the Paired Means Difference Calculator?

confidence intervala range of values so defined that there is a specified probability that the value of a parameter lies within it.differencethe result of one of the important mathematical operations, which is obtained by subtracting two numberspaired means difference

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