Why Study Statistics?

Not Everything is Deterministic What Statistics Can Do What Statistics Cannot Do What You Can Do

Bernd Schroder

Bernd Schroder Louisiana Tech University, College of Engineering and Science

Processes That Are Influenced by Randomness

Coin flips.

Processes That Are Influenced by RandomnessCoin flips.

Roulette

Processes That Are Influenced by RandomnessRoulette

Card games

Processes That Are Influenced by RandomnessCard games

Disclaimer. We will talk about games of chance as avisualization. And we certainly want to understand them. Butthere is no explicit or implicit endorsement of gambling.

Disclaimer.

We will talk about games of chance as avisualization. And we certainly want to understand them. Butthere is no explicit or implicit endorsement of gambling.

Disclaimer. We will talk about games of chance as avisualization.

And we certainly want to understand them. Butthere is no explicit or implicit endorsement of gambling.

Disclaimer. We will talk about games of chance as avisualization. And we certainly want to understand them.

Butthere is no explicit or implicit endorsement of gambling.

Disclaimer. We will talk about games of chance as avisualization. And we certainly want to understand them. Butthere is no explicit or implicit endorsement of gambling.

The frequency of accidents

Processes That Are Influenced by RandomnessThe frequency of accidents

Grade distributions

Processes That Are Influenced by RandomnessGrade distributions

Scientific measurements

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Processes That Are Influenced by RandomnessScientific measurements

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Reality itself!

Processes That Are Influenced by RandomnessReality itself!

Not All Randomness Is The Same

1. Coin flips have 2 outcomes.2. Roulette trials have 37 (or 38) outcomes.3. There are ... well, how many poker hands are there?

So far, every outcome was equally likely.4. The number of accidents can range from zero to every car

on the road. But both extremes, as well as numbers thatexceed a certain percentage, are unlikely.

So far, everything could be worked out with integers.5. Scientific measurements can return any real number. But

we would certainly hope they cluster around the actualvalue.

6. And for grade distributions, people sometimes talk about abell curve. But how do you connect a bell curve to a setwith 5 elements (A,B,C,D,F)?

Not All Randomness Is The Same1. Coin flips have 2 outcomes.

2. Roulette trials have 37 (or 38) outcomes.3. There are ... well, how many poker hands are there?

Not All Randomness Is The Same1. Coin flips have 2 outcomes.2. Roulette trials have 37 (or 38) outcomes.

3. There are ... well, how many poker hands are there?So far, every outcome was equally likely.

4. The number of accidents can range from zero to every caron the road. But both extremes, as well as numbers thatexceed a certain percentage, are unlikely.

Not All Randomness Is The Same1. Coin flips have 2 outcomes.2. Roulette trials have 37 (or 38) outcomes.3. There are

... well, how many poker hands are there?So far, every outcome was equally likely.

Not All Randomness Is The Same1. Coin flips have 2 outcomes.2. Roulette trials have 37 (or 38) outcomes.3. There are ... well, how many poker hands are there?

So far, every outcome was equally likely.

on the road.

But both extremes, as well as numbers thatexceed a certain percentage, are unlikely.

So far, everything could be worked out with integers.

5. Scientific measurements can return any real number. Butwe would certainly hope they cluster around the actualvalue.

So far, everything could be worked out with integers.5. Scientific measurements can return any real number.

Butwe would certainly hope they cluster around the actualvalue.

6. And for grade distributions, people sometimes talk about abell curve.

But how do you connect a bell curve to a setwith 5 elements (A,B,C,D,F)?

Statistics Can Tell Your Odds

1. If a fair coin is flipped sufficiently often, it should come upheads about 50% of the time.

2. If a fair roulette wheel is spun sufficiently often, thenumber 13 will show 1/37 (or 1/38) of the time.

3. Your odds for a full house ... that’s a good question!4. It’s not a game, but accident statistics are used to set

insurance rates. Statistically, younger drivers (andespecially young male drivers) are more likely to haveaccidents than older or female drivers.

5. By repeating measurements, we can obtain anexperimental average that is more reliable than a singlemeasurement would be.

6. On a national standardized test, the outcome statistics tellyou how you compare to the rest of the nation.

Statistics Can Tell Your Odds1. If a fair coin is flipped sufficiently often, it should come up

heads about 50% of the time.

2. If a fair roulette wheel is spun sufficiently often, thenumber 13 will show 1/37 (or 1/38) of the time.

heads about 50% of the time.2. If a fair roulette wheel is spun sufficiently often, the

number 13 will show 1/37 (or 1/38) of the time.

number 13 will show 1/37 (or 1/38) of the time.3. Your odds for a full house

... that’s a good question!4. It’s not a game, but accident statistics are used to set

number 13 will show 1/37 (or 1/38) of the time.3. Your odds for a full house ... that’s a good question!

4. It’s not a game, but accident statistics are used to setinsurance rates. Statistically, younger drivers (andespecially young male drivers) are more likely to haveaccidents than older or female drivers.

number 13 will show 1/37 (or 1/38) of the time.3. Your odds for a full house ... that’s a good question!4. It’s not a game, but accident statistics are used to set

insurance rates.

Statistically, younger drivers (andespecially young male drivers) are more likely to haveaccidents than older or female drivers.

Statistics Cannot Tell You Any Of the Following

1. Statistics cannot tell you if the coin will come up heads ortails in the next flip.

2. Statistics cannot tell you which number will show on thenext spin of the roulette wheel.

3. Statistics cannot tell you what your next hand of cards willlook like.But a long time ago, MIT students found a way tosufficiently improve their odds at blackjack to beat casinos.

4. Statistics cannot tell you if you are going to have anaccident. Don’t take chances and hope that no one else onthe road does either.

Statistics Cannot Tell You Any Of the Following1. Statistics cannot tell you if the coin will come up heads or

tails in the next flip.

2. Statistics cannot tell you which number will show on thenext spin of the roulette wheel.

tails in the next flip.2. Statistics cannot tell you which number will show on the

next spin of the roulette wheel.

next spin of the roulette wheel.3. Statistics cannot tell you what your next hand of cards will

look like.

But a long time ago, MIT students found a way tosufficiently improve their odds at blackjack to beat casinos.

look like.But a long time ago, MIT students found a way tosufficiently improve their odds at blackjack to beat casinos.

4. Statistics cannot tell you if you are going to have anaccident.

Don’t take chances and hope that no one else onthe road does either.

Statistics Cannot Tell You Any Of the Following

5. Statistical analysis cannot fix systematic errors in faultymeasurement equipment. If your equipment is ancient, youdon’t run thousands of repeated measurements to get a(theoretically) more reliable experimental average. Youbuy new equipment.

6. Statistics cannot predict your grade, or even the gradedistribution of this class. If everyone is well-prepared andstudies the material, the grade distribution is likely to behigh. If not, well, let’s not think about it.Make sure we stay within the first option and that we don’tslip into the second possibility. (It’s a possibility, not anoption.)

Statistics Cannot Tell You Any Of the Following5. Statistical analysis cannot fix systematic errors in faulty

measurement equipment.

If your equipment is ancient, youdon’t run thousands of repeated measurements to get a(theoretically) more reliable experimental average. Youbuy new equipment.

measurement equipment. If your equipment is ancient, youdon’t run thousands of repeated measurements to get a(theoretically) more reliable experimental average.

Youbuy new equipment.

measurement equipment. If your equipment is ancient, youdon’t run thousands of repeated measurements to get a(theoretically) more reliable experimental average. Youbuy new equipment.

6. Statistics cannot predict your grade, or even the gradedistribution of this class.

If everyone is well-prepared andstudies the material, the grade distribution is likely to behigh. If not, well, let’s not think about it.Make sure we stay within the first option and that we don’tslip into the second possibility. (It’s a possibility, not anoption.)

6. Statistics cannot predict your grade, or even the gradedistribution of this class. If everyone is well-prepared andstudies the material, the grade distribution is likely to behigh.

If not, well, let’s not think about it.Make sure we stay within the first option and that we don’tslip into the second possibility. (It’s a possibility, not anoption.)

6. Statistics cannot predict your grade, or even the gradedistribution of this class. If everyone is well-prepared andstudies the material, the grade distribution is likely to behigh. If not

, well, let’s not think about it.Make sure we stay within the first option and that we don’tslip into the second possibility. (It’s a possibility, not anoption.)

6. Statistics cannot predict your grade, or even the gradedistribution of this class. If everyone is well-prepared andstudies the material, the grade distribution is likely to behigh. If not, well, let’s not think about it.

Make sure we stay within the first option and that we don’tslip into the second possibility. (It’s a possibility, not anoption.)

6. Statistics cannot predict your grade, or even the gradedistribution of this class. If everyone is well-prepared andstudies the material, the grade distribution is likely to behigh. If not, well, let’s not think about it.Make sure we stay within the first option and that we don’tslip into the second possibility.

(It’s a possibility, not anoption.)

Statistics Can Be Confusing

1. In 1975, 20% of all drivers in fatal collisions were women.2. In 1998, 27.1% of all drivers in fatal collisions were

women.3. Did female drivers become more dangerous? Let’s not

jump to conclusions.4. Fatal collision rate per 100,000 drivers:

1975: male: 64, female: 161998: male: 43, female: 16

5. Maybe male drivers became safer? Maybe there is bettersafety equipment? The total distance driven per driver hasincreased, so, overall, roads have become safer.

Data collected from: Trends in Fatal Crashes Involving FemaleDrivers, 1975-1998, Insurance Institute for Highway Safety,July 2001.

Statistics Can Be Confusing1. In 1975, 20% of all drivers in fatal collisions were women.

2. In 1998, 27.1% of all drivers in fatal collisions werewomen.

3. Did female drivers become more dangerous? Let’s notjump to conclusions.

4. Fatal collision rate per 100,000 drivers:1975: male: 64, female: 161998: male: 43, female: 16

Statistics Can Be Confusing1. In 1975, 20% of all drivers in fatal collisions were women.2. In 1998, 27.1% of all drivers in fatal collisions were

women.

3. Did female drivers become more dangerous? Let’s notjump to conclusions.

women.3. Did female drivers become more dangerous?

Let’s notjump to conclusions.

jump to conclusions.

1975: male: 64, female: 16

1998: male: 43, female: 165. Maybe male drivers became safer? Maybe there is better

safety equipment? The total distance driven per driver hasincreased, so, overall, roads have become safer.

5. Maybe male drivers became safer?

Maybe there is bettersafety equipment? The total distance driven per driver hasincreased, so, overall, roads have become safer.

5. Maybe male drivers became safer? Maybe there is bettersafety equipment?

The total distance driven per driver hasincreased, so, overall, roads have become safer.

Always be careful to not draw unwarranted conclusions.Beware of the ways in which statistics can be abused.(According to statistics, I don’t exist.)

Statistics Can Be ConfusingAlways be careful to not draw unwarranted conclusions.

Beware of the ways in which statistics can be abused.(According to statistics, I don’t exist.)

Statistics Can Be ConfusingAlways be careful to not draw unwarranted conclusions.Beware of the ways in which statistics can be abused.

(According to statistics, I don’t exist.)

Statistics Can Be ConfusingAlways be careful to not draw unwarranted conclusions.Beware of the ways in which statistics can be abused.(According to statistics, I don’t exist.)

R. Feynman, an eminent quantum physicist, once said“I can safely say that no one understands quantum mechanics.”

So we’ve got work to do as we close in on the quantum frontier.And one of the first steps is fundamental statistics.

Statistics Can Be ConfusingR. Feynman, an eminent quantum physicist, once said

“I can safely say that no one understands quantum mechanics.”

Statistics Can Be ConfusingR. Feynman, an eminent quantum physicist, once said“I can safely say that no one understands quantum mechanics.”

So we’ve got work to do as we close in on the quantum frontier.

And one of the first steps is fundamental statistics.

Don’t Be A Statistic

And to achieve that, I recommend the following approach foreach section.

1. Read the section.2. Try the homework. All of it, every problem is different.3. Watch the presentation.4. Finish the homework.

The more you can do by reading the text, the easier technicalclasses will be.But seek help as needed. (Office hours, etc.)

Don’t Be A StatisticAnd to achieve that, I recommend the following approach foreach section.

1. Read the section.

2. Try the homework. All of it, every problem is different.3. Watch the presentation.4. Finish the homework.

1. Read the section.2. Try the homework.

All of it, every problem is different.3. Watch the presentation.4. Finish the homework.

1. Read the section.2. Try the homework. All of it

, every problem is different.3. Watch the presentation.4. Finish the homework.

1. Read the section.2. Try the homework. All of it, every problem is different.

3. Watch the presentation.4. Finish the homework.

1. Read the section.2. Try the homework. All of it, every problem is different.3. Watch the presentation.

4. Finish the homework.The more you can do by reading the text, the easier technicalclasses will be.But seek help as needed. (Office hours, etc.)

The more you can do by reading the text, the easier technicalclasses will be.

But seek help as needed. (Office hours, etc.)

The more you can do by reading the text, the easier technicalclasses will be.But seek help as needed.

(Office hours, etc.)

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