1 review definitions of statistics, population, sample, experimental unit, inference, parameter,...

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Review• Definitions of Statistics, Population,

Sample, Experimental Unit, Inference, Parameter, Statistic, Variable, Reliability.

• Sampling and Bias

• Classification of Variables (qualitative, quantitative, discrete and continuous)

• Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 in text

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Key Elements of a Statistical Problem

• Describe the population

• Describe the variable/s of interest

• Describe the sample

• Describe the inference

• Describe sources of possible errors/bias

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Example (Study 1: page 5 of text) Speed Training Program for High School Football players

• Michael Gray and Jessica Sauerbeck researchers at Northern Kentucky University designed and tested a speed training program for a junior-varsity and varsity high school football players Each participant was timed in a 40-yard sprint prior to the start of the training program and timed again after completing the program. Based on these sprint times, each participant was classified as having an “improved” time, “no change” in time, or a “decrease” in time. In a sample of 15 players selected from different schools in the area, 13 had an “improved” time. The results show that nearly 87% of players who participated in this speed training program improved their sprint times.

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Question 1.23

According to the Amer. Lung Ass., lung cancer accounts for 28% of all cancer deaths in the US. A new type of screening for lung cancer, the CT scan, has been developed. Medical researchers believe CT scans are more sensitive than X-rays in finding tumors. The Moffitt Cancer is conducting a trial of 50,000 smokers nationwide to compare the effect of CT scans with X-rays for detecting lung cancer. Each participant is randomly assigned to one of the two screening methods and their progress is tracked over time. The age at which the scanning method first detects a tumor is the variable of interest.

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Question 1.25

Does a message enable the muscles of a tired athletes to recover faster than usual? To answer this question researchers recruited eight amateur boxers to participate in an experiment. After a 10-minute workout in which each boxer threw 400 punches, half the boxers were given a 20 minute message. The other half rested. Before returning to the ring for a second workout, the heart rate and blood lactate level were recorded for each boxer. The researchers found no difference in the means of the two groups of boxers for either variable.

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Chapter 2: Descriptive Statistics

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Chapter 2: Descriptive Statistics

• Two types of variables– Qualitative– Quantitative

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Chapter 2: Descriptive Statistics

• Two types of variables– Qualitative– Quantitative

• There are different ways to represent each type of Data, but we will find there are more techniques for describing Quantitative data.

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Qualitative Data

• To describe Qualitative data we must place the data into a certain classes.

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Qualitative Data

• To describe Qualitative data we must place the data into a certain classes.

• Each class has an associated class frequency and relative frequency and class percentage.

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Qualitative Data

• To describe Qualitative data we must place the data into a certain classes.

• Each class has an associated class frequency and relative frequency and class percentage.

• Sometimes we keep track of these cumulatively.

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Example• A total of 22 StFX students were tested and

found to have the following blood types:

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Example• A total of 22 StFX students were tested and found to

have the following blood types:

Frequency is how often each class occurs

Blood Type Frequency

0 2

A 11

B 5

AB 4

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Example• A total of 22 StFX students were tested and found to

have the following blood types:

Frequency is how often each class occurs

Blood Type Frequency Cumulative Frequency

0 2 2

A 11 13

B 5 18

AB 4 22

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Example• A total of 22 StFX students were tested and

found to have the following blood types:

Blood Type Frequency Relative Frequency

0 2 2/22

A 11 11/22

B 5 5/22

AB 4 4/22

n

FrequencyFrequency Realtive

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Example• A total of 22 StFX students were tested and

found to have the following blood types:

Blood Type Frequency Percentage

0 2 9.09%

A 11 50.00%

B 5 22.73%

AB 4 18.18%

100*Frequency

Percentagen

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Example• A total of 22 StFX students were tested and

found to have the following blood types:

100*Frequency

Percentagen

Blood Type

Frequency Relative Frequency

Percentage

0 2 2/22 9.09

A 11 11/22 50.00

B 5 5/22 22.70

AB 4 4/22 18.18

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Example• A total of 22 StFX students were tested and

found to have the following blood types:

100*Frequency

Percentagen

Blood Type

Frequency Percentage Cumulative Percentage

0 2 9.09 9.09

A 11 50.00 59.09

B 5 22.73 81.82

AB 4 18.18 100.00

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Qualitative Data

• With qualitative data (and any other data we wish to separate into certain classes), tables, charts and diagrams are often the best way to present the data.

• It gives us a visual feel for the data and pictures can be more easily understood quickly and information can be passed on without technical jargon.

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Example• A total of 22 StFX students were tested and

found to have the following blood types:

100*Frequency

Percentagen

Blood Type

Frequency Percentage Cumulative Percentage

0 2 9.11 9.11

A 11 50.00 59.11

B 5 22.70 81.72

AB 4 18.28 100.00

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Example• Pie Chart

50

22.7

18.2

9.1

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Example

To find the angle of each slice, multiply relative frequency by 360 degrees.

50

22.7

18.2

9.1

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Example• Bar Graph

0

2.4

4.8

7.2

9.6

12

A B AB O

11

4

5

2

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Example

• We may also ask you to draw a histogram where the height of each bar is the class percentage or class frequency.

0

2.4

4.8

7.2

9.6

12

A B AB O

11

4

5

2

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Example• Pareto Graph – bar graph arranged from

highest to lowest.

0

2

4

6

8

10

12

A B AB O

Frequency

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Practice Exercises/SPSS

• #2.8 on page 37

• #2.14 on page 39