
Confidence Intervals
When the two population standard deviations are equal (pooled)
| 
 | 
 | α | 2 | 
 | 1 | 
 | 1 | ||
| Left = (o1 – o2)– tn1+n2  | 
 | xp  | n1 + n2 | ||||||
| 
 | 
 | 
 | 
 | ||||||
| 
 | 2 | 
 | |||||||
| Right = (o1 – o2)+ tn1+n2 | 
 | 
 | α | xp  | 
 | 1 + 1 | |||
| 
 | 
 | 
 | 
 | ||||||
| 2 | 
 | ||||||||
| 
 | 
 | 
 | 
 | n1 | n2 | ||||
When the two population standard deviations are not equal (not pooled)
| Left = (o1 – o2)– tdf | 
 | α | + | x2  | ||||
| 
 | 
 | 
 | 
 | n1 | 
 | n2 | ||
| 
 | 2 | 
 | 
 | |||||
| Right = (o1 – o2)+ tdf | 
 | α | + | x2  | ||||
| 
 | 
 | n1 | 
 | n2 | ||||
| 2 | 
 | |||||||
| df = | 
 | 
 | 1 | 
 | 
 | 
| 
 | C2 | 
 | |||
| 
 | 
 | 
 | +  | ||
| 
 | 
 | ||||
| 
 | 
 | ||||
| C = | 
 | n1 | |||
| 
 | 
 | n1 | + | n2 | 
 | 
Definition of Terms
| confidence level (0  | |
| List(1) : | list where sample 1 data is located | 
| List(2) : | list where sample 2 data is located | 
| Freq(1) : | frequency of sample 1 (1 or list name) | 
| Freq(2) : | frequency of sample 2 (1 or list name) | 
| Pooled : | On or Off | 
| o1 : | sample mean of sample 1 data | 
| x1σn−1 : | sample standard deviation of sample 1 (x1σn−1 >0) | 
| n1 : | size of sample 1 (positive integer) | 
| o2 : | sample mean of sample 2 data | 
| x2σn−1 : | sample standard deviation of sample 2 (x2σn−1 >0) | 
| n2 : | size of sample 2 (positive integer) | 
Calculation Result Output
Left : interval lower limit (left edge)
Right : interval upper limit (right edge)
df : degrees of freedom
o1 : sample mean of sample 1 data
o2 : sample mean of sample 2 data
n1 : size of sample 1
n2 : size of sample 2
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