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When testing for the difference between two population means, there are a few different situations which may be encountered. The particular situation will dictate whether to use the separate or pooled variances option. Both options assume that the samples are independent and random. They also assume that the measurement scale is at least interval (e.g., temperature or age).
If both samples are large enough (e.g., each sample with at least 30 valid observations), then the separate variances option can be used. If one sample (or both) is not large enough, then the pooled variances option should be used if the samples are each normally distributed (i.e., a type of bell-shaped curve) and the two population variances (spread) can be considered equal.
A flowchart detailing the decision process for choosing the most appropriate option is shown below:
