Question

4. The following table presents the data on comparison of three methods of determining serum amylase values in patients with pancreatitis. Test whether these data indicate a difference among the three methods.

Serum amylase values (enzyme units per 100 ml of serum) in patients with pancreatitis
Specimen	Method of determination
	A	B	C
1	4000	3210	6120
2	1600	1040	2410
3	1600	647	2210
4	1200	570	2060
5	840	445	1400
6	352	156	249
7	224	155	224
8	200	99	208
9	184	70	227

Answer 1

We have to use ANOVA to comparison of three methods of determining serum amylase values in patients with pancreatitis

Here the hypotehsis are given by

H0 : There is no significant difference between means of three methods of determining serum amylase values.

H1 : There is significant difference between means of three methods of determining serum amylase values

The ANOVA table :

Data

Specimen	A	B	C
1	4000	3210	6120
2	1600	1040	2410
3	1600	647	2210
4	1200	570	2060
5	840	445	1400
6	352	156	249
7	224	155	224
8	200	99	208
9	184	70	227

Using excell we have following output

ANOVA TABLE

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	4242888	2	2121444	1.039075	0.369159	3.402826
Within Groups	48999966	24	2041665
Total	53242854	26

There are three treatments : d.f. for between treatments = k -1 = 3-1 = 2

D.f. for total = N-1 = 27- 1 = 26

d.f. or within treatments = n-k = 26-2 = 24

We have SSwithin =48999966

So MSwithin =SSwithin /d.f. or within treatments =2041665

MSbetween =SS between /d.f. between =2121444

• SSTotal = SSBetween + SSwithin = 53242854

• We have F = MSbetween / MSwithin  =1.0390

• Here calcualted value of F=1.0390 < 3.4028=critical value of F

  Hence we do not reject null hypothesis.

  Cocnlusion :

• There is no significant difference between means of three methods of determining serum amylase values.

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