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Probabilities, the Probabilities, the Scientific Method and Scientific Method and

Religious FaithReligious FaithDon E. Bray

College Station, Texas979-492-9534

debray1@mac.com

Presentation at Christ United Methodist Church, 02/03/10

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The Scientific MethodThe Scientific Method

The term scientific method is used to describe controlled experiments where the outcomes of several repetitions may produce different results. The differences in outcomes may be attributed to experimental error, or to erroneous assumptions. The mathematical error shows the degree of agreement or disagreement with the initial assumption.

Adapted from:

http://www.britannica.com/eb/article-60609/principles-of-physical-science

Definitions Definitions

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Hypothesis – idea of broad scope, conceived by the human imagination, that encompasses a family of (experiential) laws regarding regularities existing in objects and events, both observed and posited.

Theory -is a structure suggested by these laws and is devised to explain them in a scientifically rational manner.

Fact - a thing that is indisputibly the case.Source – Encyclopedia Britannica Onlire 2010

Short Definitions Short Definitions

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•Hypothesis – an idea……...

•Theory -is a suggested structure…..

•Fact - the Sun is going to rise

The Role of ExperimentsThe Role of Experiments

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•Experiments are often performed to test hypotheses in order to develop theories

•To test a theory, we need to select the likely factors and anticipate the outcomes

•How well our predicted outcomes are confirmed by experiment indicates the validity of our theory.

Probability of a Heads in a coin Probability of a Heads in a coin flipflip

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Probability of a tails would be the same.

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P(H) =1event

number of possible events=

1

2= 0.5

Probability of getting a six from Probability of getting a six from one roll of a six sided dieone roll of a six sided die

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€

P(6) =1

6= 0.167

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Likelihoods or ProbabilitiesLikelihoods or Probabilities

Expresses likelihood of an event occurring.Expresses likelihood of an event occurring. A baseball hitter batting 0.333 will be expected A baseball hitter batting 0.333 will be expected

to get a hit once for every three times at bat.to get a hit once for every three times at bat. A baseball hitter batting 0.200 will be expected A baseball hitter batting 0.200 will be expected

to get a hit once for every five times at bat.to get a hit once for every five times at bat. These batting averages are based on the data set These batting averages are based on the data set

which is the previous batting record of the which is the previous batting record of the individual.individual.

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Using ProbabilitiesUsing Probabilities

The probability is an expectation, not an assured The probability is an expectation, not an assured result.result.

The baseball manager cannot expect that a The baseball manager cannot expect that a batter hitting 300 will always get a hit. He may batter hitting 300 will always get a hit. He may go hitless for ten at bats and then get four or five go hitless for ten at bats and then get four or five straight hits. straight hits.

A probability = 1 is assured, will always occur.A probability = 1 is assured, will always occur. A probability = 0 will never occur.A probability = 0 will never occur.

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Drawing Marbles from a Bag

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Drawing Marbles from a BagDrawing Marbles from a Bag TRUTH is the number of Solid marbles in the TRUTH is the number of Solid marbles in the

bagbag Guess the TRUTH.Guess the TRUTH. Draw five marbles at a time and record Clear Draw five marbles at a time and record Clear

and Solid marbles.and Solid marbles. Plot the distribution of Solid marbles after Plot the distribution of Solid marbles after

each draw.each draw. Compare ESTIMATED TRUTH with the Compare ESTIMATED TRUTH with the

REAL TRUTH. REAL TRUTH. 02/02/1002/02/10

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€

Cumulative Distribution =Cumulative Total for Type

Cumulative Total for Draw€

Cumulative Total = Total Quantity Drawn for Each Type

Risk of Wrong Conclusion From Risk of Wrong Conclusion From too Small of a Data Settoo Small of a Data Set

Often, we do not know the truth, we must Often, we do not know the truth, we must speculate based on available data.speculate based on available data.

Three groups were each given a bag with Three groups were each given a bag with different distribution of solid and clear marbles different distribution of solid and clear marbles (Truth). (Truth).

The next slide shows the results of their draws.The next slide shows the results of their draws. As the number of draws increases, note how As the number of draws increases, note how

the perceived difference between the three the perceived difference between the three groups changes.groups changes.

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Views from too small of a data Views from too small of a data set!set!

Neal Bortz, 03/20/08 on his broadcast cited 5 Neal Bortz, 03/20/08 on his broadcast cited 5 year ocean temperature which showed no year ocean temperature which showed no change and chortled that evidence for global change and chortled that evidence for global warming was nowhere to be seen. warming was nowhere to be seen.

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Old Farmer’s AlmanacOld Farmer’s Almanac

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Direct Plot from NASA GoddardDirect Plot from NASA Goddard

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Effect of Sample Period on Perceived Slope Effect of Sample Period on Perceived Slope (From Lord Monckton 2009)(From Lord Monckton 2009)

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14 year 10 year

6 year 2 year

Fact-Shipping lanes are opening over the Fact-Shipping lanes are opening over the Arctic Circle!Arctic Circle!

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What does this have to do with What does this have to do with your religious faith?your religious faith?

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•You might need to change some of your beliefs, given new scientific findings.

•As did John Wesley ……………..