# Correct 't-Test' to be used

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Prawns are known to lose weight after fished out of water.

I want to check claim of a firm that its product (weight gaining additive) gains weight of prawn by better water retention and absorption.

Following are characteristics of prawns to be used for experiment. These are culture prawns. All prawns used for experiment are offspring of one set of parents. (Thus, all of them have same father and mother). All of them were raised in same hatchery and fed same feed. In grow-out phase, all of them were raised in same pond, for same number of months and fed same feed.

All will be in weight range of 28 g to 30 g per individual.

Hypothesis

Ho : μ (without treatment) = μ (with treatment)

H1 : μ (without treatment) ≠ μ (with treatment)

α : 0.05

Without Treatment : In this group, weight increasing additive is NOT added. 1kg prawns and 1litre chilled water is kept in each of 15 tubs. Let us say, this is row A.

With Treatment : In this group, weight increasing additive IS added. 1kg prawns, 1 litre chilled water and weight increasing additive is added (as per dose prescribed by manufacturer) in each of 15 tubs. Let us say this is row B. Thus, we have 30 tubs of prawns for our experiment, 15 tubs in each row (row A and row B)

Both, row A and row B are arranged simultaneously and kept undisturbed for 150 minutes in the same room at same temperature. After 150 minutes, water is drained and weight gain (in percentage) is noted in prawns in each tub.

For this arrangement, can we consider A1 and B1 as one pair of tubs, A2 and B2 as second pair and so on up to A15 and B15. i.e can we say we have arranged 15 pairs of tubs with each pair having one tub without treatment and other with treatment, all other conditions being same.

Thus, if ‘t-Test: Paired two sample for means’ (t test for dependent samples) is applied , would it be correct for aim of our experiment ? Or ‘t-Test: Two-Sample Assuming Equal Variances’ should be applied ? Or ‘t-Test: Two-Sample Assuming Unequal Variances’ should be applied ?

• The additive could change the variance of the test group (some prawns may have an unexpected reaction to it) so I would say you need a t-Test for two groups where the variance is not assumed to be equal. – Morgan Ball Mar 24 '17 at 10:48