Estimating Standard Deviation Based on
Range, Interquartile Range, Confidence Interval, t-value, or P-value

Scenario 1: Conversion Based on Range or Interquartile Range (Assuming Normal Distribution)
          Range
or
Interquartile Range
Result: Standard Deviation

Calculating Standard Deviation for Paired Designs: Scenarios 2 and 3

Scenario 2: Based on Sample Size + Standard Error or Sample Size + Confidence Interval (Using t-distribution)
Sample Size (n)
Standard Error (SE)
or
confidence level

Lower Limit (L) Upper Limit (U)
Result: Standard Deviation
$$SD=SE*\sqrt{n}$$
Scenario 3: Based on Sample Size, Pre-Post Mean Difference , t-value, or P-value (Using t-distribution)
Sample Size (n)
Pre-Post Mean Difference
P value of Mean Difference
or
t value of Mean Difference
Result: Standard Deviation

Calculating Standard Deviation for Grouped Designs: Scenarios 4 and 5

Scenario 4: Based on Sample Sizes of Two Groups and Standard Error or Confidence Interval (Using t-distribution)
Sample Size of Group 1 (n1)
Sample Size of Group 2 (n2)
Standard Error (SE)
or
confidence level

Lower Limit (L) Upper Limit (U)
Result: Standard Deviation (SD)
$$SD=SE*\sqrt{1/n_1+1/n_2}$$
Scenario 5: Based on Sample Sizes of Two Groups, Mean Difference, t-value, or P-value (Using t-distribution)
Sample Size of Group 1 (n1)
Sample Size of Group 2 (n2)
Between-Group Mean Difference
P-value for Mean Difference
或
t-value for Mean Difference
Result: Standard Deviation (SD)

Reference:

[1] Rosner, Bernard (Bernard A.). Fundamentals of Biostatistics. Boston :Brooks/Cole, Cengage Learning, 2011.