Variation and Sampling
AtMyPace: Statistics
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Módulo A
True
False
Natural Variation.
Q: Natural variation occurs only in nature?
1
X
A: Natural variation occurs in nature, but it also occurs in human
behavior, manufacturing processes and other human endeavors.
Error Due to Bias.
Q: A sample is said to have bias if all members of the
2
X
population are equally likely to be selected?
A: The opposite is true – an ideal sample is one in which all
members of the population are equally likely to be sampled.
Sampling Variation.
Q: Two students were each told to take a different random
3
sample of 10 students from the same class, and find the average
weight. They got exactly the same answer. This probably
means they disobeyed instructions and used the same sample?
A: It is unlikely that two random samples will give exactly the same
mean. The phenomenon that there will be a difference between
perfectly good samples is called sampling error or sampling
variation.
Sampling Variation.
Q: Sampling error occurs because we are looking at a sample,
4
rather than a population?
5
A: If we could test an entire population we would not have any
sampling error.
Sampling Variation.
Q: We can avoid sampling error by taking a random sample?
X
X
X
A: Sampling error is unavoidable, though good sampling methods
may help reduce the effect of sampling error.
Explainable Variation.
Q: When we travel during peak time, the time taken to get
6
home is always longer than when we travel at off-peak time.
This is always the case, so is not an example of explainable
variation?
A: This is a good example of explainable variation. If we collected
our travel times to work, and compared those which were at peak
time with those at off-peak, we would be able to get some indication
of what variation is explained by peak/off-peak timing.
Explainable Variation.
X
Q: Explainable Variation. Is variation due to known factors,
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such as age, sex, nationality?
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A: Though we don’t know exactly how much variation is attributable
to known factor, we can use statistical methods to get some idea.
Natural Variation.
Q: One pair of size 8 jeans fit Emily perfectly, whereas another
pair of size 8 jeans of the same brand and style was a little
tight. This is an example of natural variation?
X
X
A: Yes. The manufacture of jeans is a process that will have a
certain degree of variation in it. It is reasonable to expect that even
jeans of the same size, brand and style may differ slightly.
Natural Variation.
Q: Because natural variation occurs we should avoid making
generalizations from one individual instance?
9
X
A: Yes. If every item in a population were identical we could know
from a sample of 1, what all the items were like. Because all the
water in a bottle will be the same we can tell from one taste what all
the water in the bottle is like. However sampling one apple from a
tree may not tell us what all the apples on the tree are like.
Error Due to Bias.
Q: When people choose to take part in a survey, this is very
10
likely to cause error due to bias?
A: Yes. For example a phone-in survey about animal welfare is
likely to attract people with strong opinions. Conclusions drawn
from such a survey are unlikely to represent the whole population.
X
#
1
Módulo B
True
Natural Variation.
Q: Natural variation occurs in human behavior, manufacturing
X
False
processes and other human endeavors?
A: Yes. Natural variation occurs in nature, but it also occurs in
human behavior, manufacturing processes and other human
endeavors.
Error Due to Bias.
Q: Two students each took a sample of 10 students from the
2
3
X
same class, and found the average weight. They got different
answers because one of the samples must have been biased?
A: No. They got different answers because the samples were
different, which they should be. This is sampling variation. If they
each chose their friends, this could cause error due to bias,
particularly if one chose football players, for example.
Error Due to Bias.
Q: A sample is said to have bias if some members of the
X
population are more likely to be selected than others?
A: Yes. An ideal sample is one in which all members of the
population are equally to sampled.
Sampling Variation.
Q: Samples of ten packets of choconutties were taken from two
4
different machines. The mean weights of the two samples were
slightly different. This shows that there is a difference between
the machines in the amount put in the packets?
X
A: No. The difference in two samples may well be due to sampling
error. Taking two samples of ten packets each from a single machine
will probably also result in two slightly different mean weights.
There may be a difference between the machines, but we can’t
assume it.
Sampling Variation.
Q: Sampling error occurs when we take a sample that is not
5
X
representative of the population?
A: No. Sampling error occurs because we are looking at a sample,
rather than a population. Even perfectly representative random
samples still have sampling error.
Sampling Variation.
Q: Sampling error is unavoidable when taking a sample, though
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taking a large samples helps reduce the effect of sampling
error?
A: Yes. Larger samples are more likely to have a range of members
of the population in them, so will be more representative of the
X
population, and thus have less effect of sampling error.
Explainable Variation.
Q: Five boys and five girls took part in a pizza-eating
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competition. The mean number of slices eaten by the boys was
quite a lot higher than the means number of slices eaten by the
girls. However one of the girls ate the most slices so this is not
an example of explainable variation?
X
A: False. This is a good example of explainable variation. Even
though there is natural variation among the girls (and one ate the
most pieces), on average the girls ate fewer slices than the boys. We
would use a test, difference of two means, to find out if this was due
to the difference between girls and boys.
Explainable Variation.
Q: Many types of statistical analysis attempts to find out how
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much variation is attributable to known aspects. We call this
explainable variation?
A: Yes. For example, we may wish to see how different training
methods compare, so we measure the outcomes and see how much of
the variation in results can be said be due to the training method.
Natural Variation.
Q: I get to work on my bike much quicker on average if I have
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a tailwind. This is an example of natural variation?
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A: No. There is an explainable variation for getting work quickly
with a tail wind, so this is explainable variation, not natural
variation.
Natural Variation.
Q: A good manufacturing process will have no natural
variation?
A: No. Natural variation is unavoidable. Some manufacturing
processes can have less variation than others, but it is usually more
costly. For example we could expect less variation in the weights of
pharmaceuticals than in confectionary.
X
X
X