Chapter 11, Problem 11.51E

To determine

To use a software to create Normal quantile plots for each of the three groups of the forest plots and explain are the three distributions roughly Normal and what are the most prominent deviations from Normality that you see.

Answer to Problem 11.51E

Yes, the three groups are roughly Normal.

Explanation of Solution

In the question, the data is given that described of the effects of logging on counts in the Borneo rainforest as:

Thus, we will use the excel to construct the Normal quantile plot by using z-scores. And the excel function used is as:

  $=\text{NORMSINV(prob)}$

So, for group one, we have the following calculation as:

Group 1	Rank	Rank proportion	Rank based z score	Group 1
16	1	=(AA81-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB81)	16
19	2	=(AA82-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB82)	19
19	3	=(AA83-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB83)	19
20	4	=(AA84-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB84)	20
21	5	=(AA85-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB85)	21
22	6	=(AA86-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB86)	22
24	7	=(AA87-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB87)	24
27	8	=(AA88-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB88)	27
27	9	=(AA89-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB89)	27
28	10	=(AA90-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB90)	28
29	11	=(AA91-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB91)	29
33	12	=(AA92-0.5)/COUNT($Z$81:$Z$92)	=NORMSINV(AB92)	33

The result is as:

Group 1	Rank	Rank proportion	Rank based z score	Group 1
16	1	0.041667	-1.73166	16
19	2	0.125	-1.15035	19
19	3	0.208333	-0.81222	19
20	4	0.291667	-0.54852	20
21	5	0.375	-0.31864	21
22	6	0.458333	-0.10463	22
24	7	0.541667	0.104633	24
27	8	0.625	0.318639	27
27	9	0.708333	0.548522	27
28	10	0.791667	0.812218	28
29	11	0.875	1.150349	29
33	12	0.958333	1.731664	33

Thus, we will select the last two column and then go to the insert tab and select the chart option and then select the plot, so the normal quantile plot is as:

  

So, for the group two we have the calculation as:

Group 2	Rank	Rank proportion	Rank based z score	Group 2
2	1	=(AG81-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH81)	2
9	2	=(AG82-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH82)	9
12	3	=(AG83-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH83)	12
12	4	=(AG84-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH84)	12
14	5	=(AG85-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH85)	14
14	6	=(AG86-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH86)	14
15	7	=(AG87-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH87)	15
17	8	=(AG88-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH88)	17
17	9	=(AG89-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH89)	17
18	10	=(AG90-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH90)	18
19	11	=(AG91-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH91)	19
20	12	=(AG92-0.5)/COUNT($AF$81:$AF$92)	=NORMSINV(AH92)	20

Thus, the result is as:

Group 2	Rank	Rank proportion	Rank based z score	Group 2
2	1	0.0416667	-1.731664396	2
9	2	0.125	-1.15034938	9
12	3	0.2083333	-0.812217801	12
12	4	0.2916667	-0.548522283	12
14	5	0.375	-0.318639364	14
14	6	0.4583333	-0.104633456	14
15	7	0.5416667	0.104633456	15
17	8	0.625	0.318639364	17
17	9	0.7083333	0.548522283	17
18	10	0.7916667	0.812217801	18
19	11	0.875	1.15034938	19
20	12	0.9583333	1.731664396	20

Thus, we will select the last two column and then go to the insert tab and select the chart option and then select the plot, so the normal quantile plot is as:

  

So, for the group three we have the calculation as:

Group3	Rank	Rank proportion	Rank based z score	Group3
4	1	=(T81-0.5)/COUNT($S$81:$S$89)	=NORMSINV(U81)	4
12	2	=(T82-0.5)/COUNT($S$81:$S$89)	=NORMSINV(U82)	12
12	3	=(T83-0.5)/COUNT($S$81:$S$89)	=NORMSINV(U83)	12
15	4	=(T84-0.5)/COUNT($S$81:$S$89)	=NORMSINV(U84)	15
18	5	=(T85-0.5)/COUNT($S$81:$S$89)	=NORMSINV(U85)	18
18	6	=(T86-0.5)/COUNT($S$81:$S$89)	=NORMSINV(U86)	18
19	7	=(T87-0.5)/COUNT($S$81:$S$89)	=NORMSINV(U87)	19
22	8	=(T88-0.5)/COUNT($S$81:$S$89)	=NORMSINV(U88)	22
22	9	=(T89-0.5)/COUNT($S$81:$S$89)	=NORMSINV(U89)	22

The result is as:

Group3	Rank	Rank proportion	Rank based z score	Group3
4	1	0.055555556	-1.593218818	4
12	2	0.166666667	-0.967421566	12
12	3	0.277777778	-0.589455798	12
15	4	0.388888889	-0.282216147	15
18	5	0.5	0	18
18	6	0.611111111	0.282216147	18
19	7	0.722222222	0.589455798	19
22	8	0.833333333	0.967421566	22
22	9	0.944444444	1.593218818	22

Thus, we will select the last two column and then go to the insert tab and select the chart option and then select the plot, so the normal quantile plot is as:

  

Thus, we can see that in the three groups the points are approximately in a straight line and increasing in nature. Thus, we can say that the three groups are approximately follows Normal distribution and they shows Normality in nature.