One method for correcting the bias in the standard error is to “pool” the two sample variances using a procedure that allows the bigger sample to carry more weight in determining the final value of the variance.
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To correct the bias in the standard error, we can use a method called "pooling" the two sample variances. This involves combining the variances from both samples in a way that allows the larger sample to carry more weight in determining the final value of the variance.
To calculate the pooled variance, follow these steps:
1. Calculate the variance of the first sample using the formula:
Variance = Sum of squared deviations / (n1 - 1), where n1 is the sample size of the first sample.
2. Calculate the variance of the second sample using the same formula but with the sample size of the second sample, n2.
3. Calculate the pooled variance using the formula:
Pooled Variance = [(n1 - 1) * Variance 1 + (n2 - 1) * Variance 2] / (n1 + n2 - 2), where Variance 1 and Variance 2 are the variances calculated in steps 1 and 2.
By pooling the variances, we give more weight to the sample with a larger sample size. This correction helps to reduce bias in the standard error estimate, leading to more accurate inferences and hypothesis testing.