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Statistical Studies

Describing and Analyzing Experiments

In an experiment, data is collected from two or more groups and compared using statistical methods. The purpose of an experiment can be to uncover relationships between variables or to determine cause and effect.


Controlled Experiment

In a controlled experiment, the purpose is to study the effect of one specific variable or treatment. The participants are divided into two groups. Both groups are kept under the same conditions with the exception of one group — the treatment group — undergoing the treatment. The other group is called the control group.



To ensure an experiment is reliable, it's important that sampling is random. This implies that the participants of the experiment are randomly assigned to the treatment and the control group, which reduces the risk of bias and produces groups with similar characteristics.

Not randomized.svg

For example, a control group with ten men and a treatment group with ten women might not be reliable. This is because, any results could be contributed to the difference in gender rather than the treatment itself. Instead, the test subjects should be randomly assigned to each group so there are the same number of men and women.


The development team at the company WoofWoof has created a new dog food. The developers claim it makes the hair of dogs grow faster. To see if it works, they've designed an experiment. They let 10 dogs from a dog breed with short hair eat only the new food. At the same time, 10 dogs from a breed with long hair only eat the normal food. State the experiment's:

  • hypothesis
  • treatment
  • control and treatment group

Finally, determine if the test subjects are randomly assigned to the treatment and the control group.

Show Solution
From the description of the experiment, we can identify the different parts asked in the question. Let's start with the hypothesis.



In this example, the company says that the new dog food makes the hair of the dogs grow faster. Since the effect of the food is unknown, and the goal of the experiment is to determine the effect, the hypothesis is that the food makes hair grow faster.



The treatment is the variable that is changed for a group in an experiment. In this case, the changed factor is the new food. Therefore, it is the treatment of the experiment.


Control and treatment group

Because the treatment is the new food, the group of short-haired dogs is the treatment group. The group of long-haired dogs is the control group.



Randomization is used to get similar characteristics in the control and treatment group. The control group consist of dogs with long hair and the treatment group only have dogs with short hair. Neither group represents the whole population. Therefore, the experiment is not random.


Analyzing Data from an Experiment

After an experiment has been conducted, it is necessary to analyze the data. The results obtained from the treatment group are compared with the data from the control group. For example, see the results from an experiment that studies the growth of seedlings from irradiated apple seeds. Five seeds were irradiated — exposed to radiation — and then planted. The data is compared with a control group of five non-irradiated seeds.

Seedling length (cm)
Treatment group 18.5 17.5 16.3 16.6 18.5
Control group 20.2 16.1 14.5 22.7 20.1
The data can be analyzed by calculating the mean growth length of each group.
The mean growth length of the treatment group is shorter than for the control group. By subtracting the means it's possible to find how much the average growth length was affected.
The seedlings from the irradiated seeds are, on average, 1.24 cm shorter than those in the control group. From this, it could be concluded that the radiation exposure stunts growth. Another method to compare the results is to present the measurements in two dot plots, one for each group.
It can be seen that the range for the treatment group is much smaller than that for the control group. It could be concluded that the radiation exposure streamlines seed growth. No matter which analysis is used, the results might not be reliable. This is because the sample size is small. Therefore, it is difficult to draw conclusions from the experiment.



Replication is a method to increase the validity of experiments. This is done by repeating an experiment several times under conditions that are identical to that of the original experiment. The results from the new studies can then be analyzed together with the previously collected data. With more data, the results are more reliable.


Making Inferences in Statistics

Making inferences involves using data from a sample to draw conclusions or make predictions about a population. There is always some degree of uncertainty when the results from a study are used to make inferences. However, increasing the size of the sample reduces uncertainty.
Below, the recorded lengths of 100 irradiated and 100 non-irradiated apple seeds are shown.

Length (cm) Treatment group Control group
89.9 2 0
1011.9 10 0
1213.9 14 4
1415.9 18 14
1617.9 28 31
1819.9 18 28
2021.9 6 20
2223.9 4 3
The average length of the seedlings in each group can be found.
Thus, seedlings from irradiated seeds can be assumed to grow, on average, about 2 cm less when exposed to radiation. Another way to study the effects of the treatment is to present the data sets in histograms.
When the histograms are shown together, it's possible to see that the spread of the data of the treatment group is larger than that of the control group. This could mean radiation exposure stunts growth. Because the sample size in this experiment is relatively large, one can claim that the results are reliable.
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