Question

The response time in milliseconds was determined for three different types of circuits in an electronic calculator. The results are recorded in table:

Curcuit Type	Response (R)	R	R	R	R
1	19	22	20	18	25
2	20	21	33	27	40
3	16	15	18	26	17

(a) What is the value of LSD? Use α=0.01.
Round your answer to two decimal places (e.g. 98.76).

(b) Apply Fisher's LSD method with α=0.01 and state which circuit type differs or circuit types differ.

(c) What is the absolute value of difference between means for circuits 1 and 3?
Round your answer to one decimal place (e.g. 98.7).

(d) Estimate the standard error for comparing the means using the graphical method.
Round your answer to three decimal places (e.g. 98.765).

Answer 1

a)

To calculate the Least Significant Difference value, the one way ANOVA table is obtained in excel by following steps,

Step 1: Write down the data values for circuit types. The screenshot is shown below,

Step 2: DATA > Data Analysis > ANOVA: Single Factor.

Step 3: Input Range: selct all the data values, Grouped by: Columns, Alpha = 0.01. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

From the ANOVA table,

DFW = 12, MSW = 32.56667, n1 = 5, n2 = 5

The t value is obtained using the t distribution table, for significance level = 0.01, df = 12.

t = 3.05454

b)

The Fisher's LSD method is applied in following steps,

Step 1: Calculate the mean for each groups,

	Circuit 1	Circuit 2	Circuit 3
	19	20	16
	22	21	15
	20	33	18
	18	27	26
	25	40	17
Mean	20.8	28.2	18.4

Step 2: There are three possible pairwise comparison.

Comparison	Absolute mean difference
Circuit 1-circuit 2	7.4
Circuit 1-circuit 3	2.4
Circuit 2-circuit 3	9.8

Step 3: Decision Rule:

Reject the null hypothesis if,

Step 4:

Comparison	Absolute mean difference		LSD	Result
Circuit 1-circuit 2	7.4	<	11.02459	No significant difference
Circuit 1-circuit 3	2.4	<	11.02459	No significant difference
Circuit 2-circuit 3	9.8	<	11.02459	No significant difference

c)

Comparison	Absolute mean difference
Circuit 1-circuit 3	2.4

d)

	Circuit 1	Circuit 2	Circuit 3
	19	20	16
	22	21	15
	20	33	18
	18	27	26
	25	40	17
Mean	20.8	28.2	18.4
SD	2.774887	8.408329	4.393177

Standard error for difference in mean is,

Comparison	SE
Circuit 1-circuit 2	3.960
Circuit 1-circuit 3	2.324
Circuit 2-circuit 3	4.243