19 The usual treatment of hypothyroidism involves daily thyr

19. The usual treatment of hypothyroidism involves daily thyroid replacement with levothyroxine (L-T4). Optimal therapy is monitored by measurement of serum TSH. The normal thyroid gland secretes both levothyroxine (L-T4) and levotriiodothyronine (L-T3). It is generally believed that treatment L-T4 alone results in normal levels of serum L-T3 to achieve a euthyroid state. Some studies suggest, however, that patients feel better when taking an L-T4/L-T3 combination compared with L-T4 alone.
Woeber (2002) wished to study this clinical issue further by evaluating the effect of L-T4 replacement therapy on serum free T4. He studied the relationship in a historical cohort of patients with chronic autoimmune thyroiditis and a group of normal individuals. Woeber\'s data gave the following results.

At the 1% level, is there a difference in the mean free T4 equal among the three groups of subjects.  Why or why not?

Is there a difference in the average ?  Explain. If needed, you may use a 95% level of confidence.

You must type the following here - they must match what is on your work:
1. Test statistic, critical value or p-value, decision, and interpretation.
2. Confidence interval end points and decision.

Solution

SSB = SST - SSW = 84

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dfB = number of groups - 1 = 3 - 1 = 2

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dfW = number of participants - number of groups

=(20 + 18 + 35) - 3

= 70

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dfT = dfB + dfW = 70 +2 = 72

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MSB = SSB / dfB = 42

MSW = SSW/dfW = 3.5213

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F = MSB/MSW = 11.927

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Decision:

As P < 0.01, WE REJECT THE NULL HYPOTHESIS.

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Conclusion:

There is a signficant difference between the groups.