### Statistics Fundamentals

Statistics is such a powerful tool because it uses data to convey important information. This information may be visualized as a graph, chart, or table. It might be given numerically as the mean, median, mode, or percent change. There are so many different ways to frame information.

Because people can choose how to show statistics, sometimes it can be deceiving. Let's look at some examples.

# Deception

From the data above, what can we conclude about home prices in the United States? Select all that apply.

# Deception

Select one or more

A study is done on 250 people who claim they have psychic abilities.

A regular deck of cards has an equal number of red and black cards. The deck is shuffled, and each person predicts the color of the top card. The top card is then flipped face up to see if they are correct. This is repeated 8 times in a row.

One participant gets all 8 predictions correct! The researcher claims that this person has exhibited psychic abilities.

Based on just the way the experiment is designed, is the researcher's claim a viable hypothesis? (Note: we're not judging the plausibility of psychic ability in itself, just this particular experiment's design.)

# Deception

Deception in statistics can be quite intentional. In the first problem, the choice of what months to display did not happen by accident! The researcher probably wanted to convey the data in a certain way.

Deception can also be unintentional. In the second problem, the researcher examining psychic phenomena may have been earnest about their hypothesis, but they still interpreted the results of their experiment poorly.

Alternatively, sometimes the statistics themselves can deceive. It depends who gathers the data and how they do it. The questions that follow will demonstrate this issue.

# Deception

The Transportation Association of Canada wanted to study the effects of wearing a helmet on motorcycle accidents. The data below was collected by Canadian hospitals between 2002 and 2014. Each motorcyclist who was in a traffic accident and arrived at a hospital had the information below recorded.

 Wearing helmet? Yes No Arrived in ambulance 18% 9% Had concussion 9% 3% Needed blood transfusion 0.8% 0.4%

Based on the table, what is true?

A. Motorcyclists who came to a Canadian hospital that were wearing helmets in traffic accidents were twice as likely to arrive in an ambulance than motorcyclists who were not wearing helmets.

B. Motorcyclists who came to a Canadian hospital that were wearing helmets in traffic accidents were three times as likely to have a concussion than motorcyclists who were not wearing helmets.

C. 0.8% of all Canadian motorcycle riders who wear helmets will need a blood transfusion.

(Data source: Journal of Internal Medicine.)

# Deception

The previous problem showed how it is important to remember the data source. Not everyone who gets in an accident goes to the hospital!

The table below shows all motorcycle accidents in Canada between 2002 and 2014.

Which quadrants would be missing from the hospital's data?

# Deception

The data from the previous two questions demonstrates what's known as Berkson's bias. In taking what appears to be a representative sample, a specific group may still be excluded. Hospitals won't see those who are healthy enough to not need a hospital, so the data won't include this part of the population.

Recall that the table below shows all motorcycle accidents in Canada between 2002 and 2014.

Look at all accidents involving motorcyclists wearing helmets. What percentage of these accidents did the hospital see?

# Deception

Statistics cannot be done in a mathematical vacuum. Usually it involves real-life knowledge about the circumstances. This can be as important as any sort of calculation.

When looking at graphs or charts, it is important to inspect the axes and labels. When analyzing data, it is important to remember the data source and how the data was collected. This can help you recognize deceptive statistics.

It may seem, at this point, that statistics can only serve to confound. However, you'll find statistics can be used to pierce deception rather than just create it — continue the course to find out how!

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