Page 126 - Data Science class 11
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Based on the results produced, the students might have come up with few questions:
a. Was there proof that 12 hours of light and 12 hours of dark group had a significantly higher mean length than the
24 hours of light group?
b. Was there proof that 24 hours of dark group had a significantly higher mean length than the 12 hours of light and
12 hours of dark group?
c. Were these differences in mean large enough to rule out their occurrences by chance as a possible clarification
for the observed difference?
The mean length of the seedlings in the Treatment 2-Mixed group was 6.2 mm more than the treatment 1 Light
group's mean length. Even though there was a difference of 6.2 mm, it might not be massive enough to rule out
chance, and so it might become difficult to claim a treatment effect.
This noticeable difference might have been due to one bag being fortunate enough to get a large count of good
seeds. It could also be due to the light and water not being uniformly distributed among the treatment groups. But
if a difference this large (6.2 mm) was probably the result of the randomisation of seeds, then differences of such
magnitude would have been observed quite often, if the measurements were rejumbled and a new difference in
observed mean was calculated.
The students could have mocked this rejumbling by noting down each seedling's length on a separate card. Thus, for
the 56 seedlings, there would have been 56 cards. These cards would then be shuffled and divided into two piles of
28 cards each. The first pile would represent the 1-Light treatment group and the second pile would represent the
2-Mixed treatment group. The students would have then computed the difference in mean between the two piles.
The difference generated this way would have been entirely due to chance. By repeating the above process multiple
times, the student would have been able to interpret how the difference in mean varies when the treatment has no
effect on the growth of the seedlings.
Figure 2.4.4 shown herewith was produced when technology was used to mix the growth measurements from 1-Light
treatment and 2-Mixed treatment together and haphazardly divide the measurements into two groups of 28.
30.00
25.00 Line at 6.2 mm
20.00
15.00
10.00
5.00
0.00
–3.6 –3.4 –3 –2.6 –2 –1.4 –0.8 0 0.7 1.3 2.7 3 3.8 4.6 6 6.2
Figure 2.4.4 Difference in means of radish seedlings (Line at 6.2 mm)
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