From the 2 number sets that you entered, calculate a 90% confidence interval for the difference of data dCalculate the difference of means by subtracting each respective element from both data sets
x01 - x02 = 312 - 300 = 12x11 - 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 = 1945.7891d = (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 = √s2s = √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
You have 1 free calculations remaining
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 - 1α = 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 differenceTags:
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