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Week 3 Lecture Statistics For Decision Making

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Week 3 LectureStatistics For Decision Making

B Heard

Not to be used, posted, etc. without my expressed permission. B Heard

- Your Week 3 Quiz is on material covered in Weeks 1 and 2
- Your Week 5 Quiz is on material covered in Weeks 3 and 4
- Your Week 7 Quiz is on material covered in Weeks 5 and 6
- Your Final Exam is comprehensive covering the material in the three prior quizzes plus the material covered in Week 7
- Your best approach for preparing for the quizzes should be the Practice Quizzes offered in the previous week (for this week’s quiz the Week 2 Practice Quiz) and the live lecture of the Week the actual Quiz is posted

Not to be used, posted, etc. without my expressed permission. B Heard

Some Key Thoughts….

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- Name and define and discriminate between the two major branches of statistics (descriptive and inferential).
- Define major terms and discriminate between a sample and a population.
- Identify examples of the four levels of data and describe the characteristics of each data type.

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You should know the difference between the methods of collecting data.

- Sampling (collecting data from part of a population)
- Census (collecting data from the entire population – be careful because you can often do this with small groups such as number of vehicles members of the class own, average salary of the class, number of children per house on your street, etc.)
- Simulation (Using probabilities to get your results, for example the probability of getting 3 heads in 5 flips of a coin, number of boys out of 5 children, etc.)
- Perform an experiment ( often uses things like a control group like researchers giving one group the real medication and the other something that has no effect)

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You should be able to identify levels of measurement

- Nominal (just a name as in colors, types, number on a jersey, etc.)
- Ordinal (Categories that can be ranked meaningfully)
- Interval (Distance between values has meaning but there is no “absolute zero” like in the Fahrenheit temperature scale”
- Ratio (has an “absolute zero” like the number of children you have, etc. always ask yourself is the lowest possible value zero or none? If so it is probably ratio, if it can go below zero like distance above or below sea level it would be Interval)

Chart taken from

http://www.socialresearchmethods.net/kb/measlevl.php

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Know the difference between inferential and descriptive statistics.

- Descriptive statistics are used to reveal patterns through the analysis of numeric data (collect non-numeric data and then analyze).
- Descriptive statistics, not surprisingly, "describe" data that have been collected. Commonly used descriptive statistics include frequency counts, ranges (high and low scores or values), means, modes, median scores, and standard deviations.

- Inferential statistics are used to draw conclusions and make predictions based on the analysis of numeric data.
- Inferential statistics are used to draw conclusions and make predictions based on the descriptions of data.

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- Descriptive and Inferential Statistics (additional resources)
See the following links:

- http://infinity.cos.edu/faculty/woodbury/Stats/Tutorial/Data_Descr_Infer.htm(has some questions and answers)
- http://www.habermas.org/stat2f98.htm
- http://www.mdx.ac.uk/WWW/STUDY/glonumst.htm

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Know the difference between quantitative and qualitative data

- Quantitative (numbers with meaning)
- Qualitative (Colors, types, etc. and numbers without meaning)

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Know the difference in Sampling Techniques

- Random (simply picking where every member has an equal chance – drawing out of a bag – generating random numbers)
- Stratified (dividing your population into strata and then picking a certain number from each strata)
- Systematic (picking every nth one – for example testing every 20th unit off of an assembly line)
- Convenience (just asking who is available or who is listening, not making an effort to get a true sample)
- Cluster (dividing the population into clusters and sampling everyone in one or two of the clusters)
Understand the relationship between a Sample and a Population

- A sample is a subset of a population
- Sampling is more convenient and easier
- Statistics come from Samples
- Parameters come from the population (key word “all”)

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Some questions….

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A) The following table represents the weights of a number of third graders:

WeightFrequency

58-622

63-673

68-725

73-777

78-8211

83-8710

88-924

93-972

Total 44

Be Able to:

Give the relative frequencies of each class

Identify the Class Width

Identify the midpoint of the last class

Identify the class boundaries

Not to be used, posted, etc. without my expressed permission. B Heard

WeightFrequencyRelative Freq*Relative Freq(decimal)*

58-6222/440.0455

63-6733/44 0.0682

68-7255/440.1136

73-7777/440.1591

78-821111/440.2500

83-871010/440.2273

88-9244/44 0.0909

93-9722/440.0455

Total 44

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Identify the Class Width

Class width is 5 because each class contains five members (first class for example contains 58,59,60,61, and 62) or you can simply the “ending value of the first class “62” from the ending value of the second class “67” (67-62 = 5)

Identify the midpoint of the last class

60 because (97+93)/2 = 95

Identify the class boundaries

Simply subtract .5 from the lower and add .5 to the upper

57.5-62.5, 62.5-67.5, 67.5-72.5, 72.5-77.5, 77.5-82.5, 82.5-87.5, 87.5-92.5, 92.5-97.5

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The salary data (in thousands) for Bobby Statz’ first 8 years of his career are 25, 28, 32, 36, 41, 48, 51 and 53

Display the data in a stem and leaf plot.

Find the mean.

Find the median.

Find the mode.

Find the range.

Find the standard deviation.

Find Q1, Q2, Q3

Not to be used, posted, etc. without my expressed permission. B Heard

Stem and leaf plot for Bobby Statz’ salary data

2|58

3|26

4|18

5|13

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Not to be used, posted, etc. without my expressed permission. B Heard

The water level in inches of 10 randomly selected locations in a pond were taken and were as follows: 28, 37, 42, 42, 47, 52, 57, 57, 60, and 62

Display the data in a stem and leaf plot.

Find the mean.

Find the median.

Find the mode.

Find the range.

Find the range.

Find the standard deviation.

Find Q1, Q2, Q3

Not to be used, posted, etc. without my expressed permission. B Heard

Stem and leaf plot for water level data

2|8

3|7

4|227

5|277

6|02

Not to be used, posted, etc. without my expressed permission. B Heard

Find the mean.

48.5 using average function in Excel

Find the median.

50.0 using median function in Excel

Find the mode.

Bimodal, both 42 and 57

Find the range.

Highest value – lowest value = 62-28 = 34

Find the variance.

Using sample variance function in Excel (because these were randomly chosen samples) 124.28 (using “VAR” function)

Find the standard deviation.

Square Root (124.28) = 11.15 (or use “STDEV” function)

Find Q1, Q2, Q3

42, 50, 57 respectively using the quartile function in Excel

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As an instructor, I have been collecting data to see if I can model a student’s performance on a standardized entrance exam. I determined that the multiple regression equation y = -250+ 16a + 30b, where a is a student’s grade on a quiz, b is the student’s rank on a class list, gives y, the score on a standardized entrance exam. Based on this equation, what would the standardized entrance exam score for a student who makes a 7 on the quiz and had a ranking of 10 be?

Not to be used, posted, etc. without my expressed permission. B Heard

y = -250+ 16a + 30b

Substitute 7 for “a” and 10 for “b”y = -250+ 16*7 + 30*10y = -250 + 112 + 300y = -250 + 412y = 162

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In my previous example, I determined that the r^2 value (r squared) was .921. What does this tell me? What if my “r” (correlation coefficient) was .654? What would this say?

Not to be used, posted, etc. without my expressed permission. B Heard

In my previous example, I determined that the r^2 value (r squared) was .921. What does this tell me? What if my “r” (correlation coefficient) was .654? What would this say?

You could say "About 92.1% of the variation in student’s standardized entrance exams can be explained by the score of the quiz and their rank on the class list. The other 7.9% of the variation is either unexplained or is due to other things.

As far as the “r” being .654 , I would say that I have a moderately strong positive correlation.

Not to be used, posted, etc. without my expressed permission. B Heard

This data shows the Lab Report scores of 8 selected students and the number of hours they spent preparing their Statistics Lab Report. 40 was the highest score the student could make.

(hours, scores),

(3,34), (2,30), (4,38), (4,40), (2,32), (3,33), (4,37), (5,39)

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- Find the equation of the regression line for the given data.
- What is the r2 for the data?
- What is the r for the data?
- What does correlation say about causation?
- Predict a Lab Report Score for someone who spent one hour on it.

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Predicted score for someone who spent one hour would be:

y = 3.158(1) +24.71

y = 27.9 or I would say 28 since all scores are in whole numbers

Also, correlation says nothing about causation!

Not to be used, posted, etc. without my expressed permission. B Heard

- For the previous set of data find the sum of the x’s, sum of the x’s squared, and sum of the x-squareds. Display your results and label in Excel.

Not to be used, posted, etc. without my expressed permission. B Heard

It would be a good idea to be able to discuss how these relate to the correlation coefficient (see formula).

Not to be used, posted, etc. without my expressed permission. B Heard

Stronger Negative Correlation

Stronger Positive Correlation

-1

0

+1

“r”

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S

STAT CAVE

See you next week:

“Same Stat Time, Same Stat Channel”

Not to be used, posted, etc. without my expressed permission. B Heard