KINE 5305 Applied Statistics in Kinesiology
Homework #2
Analyze the data in Table 1.1 below using the SPSS Explore command.
1.Add 46 to each data point and do a natural log transformation. Then report the data as log transformed data.
2.Use some rationale to justify either the -44 or the -44 & -2 as outliers, remove them from the data set.
For both 1 & 2 above, run Kolmogorov-Smirnov goodness-of-fit test and the Shapiro-Wilk Normality test. Include a table with mean, sd, variance, skew and kurtosis. Use the journal format write-up similar to Homework 1.
The Section Below is from Moore DS, McCabe GP. Introduction to the Practice of Statistics. W.H. Freeman and Company: New York, 2nd Ed. 1993. pp3-4.
Light travels fast, but it is not transmitted instantaneously. Light takes over a second to reach us from the moon and over 10 billion years to reach us from the most distant objects yet observed in the expanding universe. Because radio and radar also travel at the speed of light, an accurate value for that speed is important in communicating with astronauts and orbiting satellites. An accurate value for the speed of light is also important to computer designers because electrical signals travel only at light speed.
The first reasonably accurate measurements of the speed of light weremade a little over 100 years ago by A. A. Michelson and Simon Newcomb. Table 1.1 contains 66 measurements made by Newcomb between July and September 1882.
Measurement
A set of numbers such as those in Table 1.1 is meaningless without some background information. We must ask several preliminary questions about any set of data. First, What variable is being measured? Newcomb measured how long light took to travel from his laboratory on the Potomac River to a mirror at the base of the WashingtonMonument and back, a total distance of about 7400 meters. Just as you can compute the speed of a car from the time required to drive a mile, Newcomb computed the speed of light from the travel time.
Answering the question "What variable is being measured?" requires a description of the instrument used to make the measurement. Then we must judge whether the variable measured is appropriate for our purpose. This judgment often requires expert knowledge of the particular field of study. For example, Newcomb invented a novel and complicated apparatus to measure the passage time of light. We accept the judgment of physicists that this instrument is appropriate for its intended task and more accurate than earlier instruments.
TABLE 1.1 / Newcomb's measurements of the passage time of light28 / 22 / 36 / 26 / 28 / 28
26 / 24 / 32 / 30 / 27 / 24
33 / 21 / 36 / 32 / 31 / 25
24 / 25 / 28 / 36 / 27 / 32
34 / 30 / 25 / 26 / 26 / 25
-44 / 23 / 21 / 30 / 33 / 29
27 / 29 / 28 / 22 / 26 / 27
16 / 31 / 29 / 36 / 32 / 28
40 / 19 / 37 / 23 / 32 / 29
-2 / 24 / 25 / 27 / 24 / 16
29 / 20 / 28 / 27 / 39 / 23