Question

In the production process of growing Azaleas, the plants are transplanted from a small pot to a larger pot. Lee’s green thumbs have realized that the newly transplanted azaleas seem to have better chance of growing to be large and healthy if they are transplanted immediately after the plant has had a major growth spurt. Therefore, they started looking at growth rates of the plants. They studied the growth of 10 plants for five periods.

Can you determine if one period is a better for transplanting than another period? Test at a 0.05 level of significance. Conduct a multiple comparisons test using Turkey’s method. Which week has the most growth? Which week has the least growth? Produce a main effects plot and an interval plot.

The data is as follow:-

Plant	Period-1	Period-2	Period-3	Period-4	Period-5
1	1.58	1.09	1.00	2.22	1.20
2	1.62	1.03	1.00	2.40	1.40
3	2.04	1.00	1.07	2.47	1.34
4	1.28	1.23	1.18	1.85	1.00
5	1.43	1.13	1.34	2.50	1.20
6	1.93	1.15	1.25	1.20	1.10
7	2.20	1.03	1.26	1.33	1.10
8	1.96	1.09	1.03	2.40	1.06
9	2.23	1.00	1.12	2.23	1.17
10	1.54	1.00	1.26	2.57	1.25

(Example interpretation of the data: the 1.58 would be interpreted as: “at the end of the first period, the plant is 58% larger than at the beginning of that same period”.)

Answer 1

One-way ANOVA: Period-1, Period-2, Period-3, Period-4, Period-5

Method

Null hypothesis         All means are equal
Alternative hypothesis At least one mean is different
Significance level      α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor       5 Period-1, Period-2, Period-3, Period-4, Period-5

Analysis of Variance

Source DF Adj SS   Adj MS F-Value P-Value
Factor   4   8.557 2.13918    27.35    0.000
Error   45   3.520 0.07822
Total   49 12.077

Model Summary

       S    R-sq R-sq(adj) R-sq(pred)
0.279682 70.85%     68.26%      64.02%

Means

Factor     N    Mean   StDev       95% CI
Period-1 10   1.781   0.333 ( 1.603, 1.959)
Period-2 10 1.0750 0.0775 (0.8969, 1.2531)
Period-3 10 1.1510 0.1238 (0.9729, 1.3291)
Period-4 10   2.117   0.493 ( 1.939, 2.295)
Period-5 10 1.1820 0.1244 (1.0039, 1.3601)

Pooled StDev = 0.279682

p-value = 0.000 < 0.05

hence there is significant difference between 5 period

Period 1 is better than other period