Chp 8 Enumerative Induction PDF

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Chp 8 Enumerative Induction

E.g. 40% of

around Kelowna are infested with pine

Therefore, about 40% of pine trees in BC are infested with pine beetles. - pine trees in BC Sample - pine trees in Kelowna Text Property - infested with pine beetles

Text

Text

Inductive - Probably Conclusion

With inductive generalizations information is taken about a sample and conclusions are made about a larger group. Problems arise if the

represent the group.

The problems that occur with enumerative inductions are: Take information from a sample and applying it to a large group

1) The size of the sample is too small to justify the conclusion (hasty generalization), 2) The sample is biased. That is, the sample group does not represent the relevant properties that are found in the target group. 3) Psychological problems arise because of how information is taken from the sample group. Text

Sample Size The size of the sample needed to justify a conclusion will depend on what is concluded. 35% of the students in the class will vote in the next election.

Thus, we expect that 35% of the students at Uvic will vote in the next election. 35% of the students in the class will vote in the next election. Thus, 35% of residents of Victoria will vote in the next election.

A small sample may prove adequate if the sample group has to represent the target group. The two rabbits in my backyard love to eat clover. Thus, most rabbits love to eat clover. Two people on my street bike to work. Thus, most people bike to work. Representativeness Example Say that you would like to make a conclusion about how students at UVic feel about allowing sororities/fraternities on campus. In order for your argument to be strong, the p you pick . That is, the as the target group.

Which of the following properties would be important? - where a student lives - a student’s major - financial resources available to the student

- student’s grade point average - student’s favorite kind of music The sample is representative when the proportions of these relevant properties are the same as with the target group. A biased sample does not have the same proportions. A sample can be made representative by: -

members so they have the

- choosing a random sample (That is, choose by some property that is not relevant.) 

A sample is random i has an

member of the

Would a sample taken from 2nd year UVic students be random? E.g. - Quality control engineer at a pudding plant picks the top pudding cup in each box - Polling for the political opinions of Canadians, choose members from the telephone book - Polling for the political opinions of Canadians, ask people to send in a questionnaire E.g.

Jack is to fraternities/sororities on campus. Jill is of /sororities on campus. Wendle is opposed to fraternities/sororities on campus.______________________ of Uvic students are to fraternities/sororities on campus.

To

we could:

- increase the sample size - make the conclusion weaker, ‘At least half of Uvic students are opposed to allowing sororities/fraternities on campus.’ The is the difference between the relative frequencies of some characteristic in the sample versus the population. of students at Uvic are opposed to fraternities/sororities +/- 5%.

The margin of error tells us

is. how general or specific

The confidence level is the represents the target group.

that the sample group

66% of students at Uvic are opposed to fraternities/sororities +/- 5% to a confidence level of 95% (or 19 times out of 20).

The confidence level tells us how strong the inductive argument is. Text

If we increase the sample size but leave the margin of error alone, what happens to the confidence level? If we leave the sample size alone but decrease the confidence level, what happens to the margin of error?

If we decrease the margin of error, but leave the confidence level the same, what change must occur with the sample size?

Psychological Factors The responses in a poll may be skewed because of how the

Do you want to support a bill that limits your freedom to own hand guns? Text

Do you want to support a bill that protects families from violence associated with guns?

Who asks the questions can also change the results. Door – to – door vs written questionnaires Reduce this effect with “double-blind” studies. Neither the surveyor nor the respondent know what the “right” answer is.

The order of the questions can also effect the result. How do you feel about Canada having the highest level of taxes in North America? What is your approval rating of the Prime Minister? Restricted choices Do the courts deal too harshly with young offenders or not harshly enough?

Ann Landers caused a stir when she announced the results of a mail poll that asked her women readers to respond to the following question: Would you be to be and treated tenderly, and forget about “the act”? Here readers were instructed to answer “Yes” or “No” and indicate whether they were over (or under) forty years of age. Over 10 thousand readers responded. The result was that 72 percent of the respondents answered “Yes”, and of those who answered “Yes”, 40 percent indicated that they were under forty years of age. Ann Landers expressed surprise that so many of those who answered “Yes” came from the under-forty group. But for her, “the greatest revelation” was “what the poll says about men as lovers. Clearly, there is trouble in paradise”. Name three different sources of bias.

Meaning of Average The mean is the arithmetic

Number of People 2 4 5

Age 18 19 20

Mean average = (2 x 18) + (4 x 19) + (5 x 20) (2 + 4 + 5)

= 19.3

The mode is the value that occurs most often.

The median is the ascending order. Number of People 2 4 5

when the values are arranged in Age 18 19 20

The (occurs 5 times) and the above it and below).



(5 values

If you are told that your grade in this course is average, which average is probably most beneficial to you?

If you are buying a house for your family and are told that the average number of bedrooms in this complex is three, which average would be best?

You are in an elevator that can take a maximum of 1500 lbs and is presently holding 10 people. If the average weight of each person is 150 lbs, what average is best?

Dispersion 

The dispersion tells us a numerical value.



The

is the number.

is in regards to

the

and the

Victoria and Winnipeg have temperatures The temperature range in Victoria 30C whereas it is 70C in Winnipeg.

.



The and the are ways to measure how the data points vary or deviate from the mean average.

Variance 2 =  (x – mean)2 n n = number of data pts Standard Deviation  = v2



If the variance or standard deviation is less, then the data points are grouped closer to the mean.



If you have a normal distribution, 2/3rds of the data points will be within one standard deviation of the mean. 95% of the data points will be within two standard deviations....