${S}_{p}=\sqrt{\frac{\left({n}_{1}-1\right)\text{\hspace{0.17em}\hspace{0.17em}}{s}_{1}^{2}+\text{\hspace{0.17em}}\left({n}_{2}-1\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}{s}_{2}^{2}}{\left({n}_{1}+{n}_{2}-2\right)}}$

Description:

Math equation. The pooled estimate of the common standard deviation (Sp) is the square root of a quotient. The numerator of the quotient is the sum of first sample size minus 1 times the square of the first sample's standard deviation plus the second sample's sample size minus 1 times the square of the second sample's standard deviation. The denominator for the quotient is the sum of the two sample sizes minus 2.