Transcript Intro to Statistics

Intro to Statistics and SPSS
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Mean (average)
Median – the middle score (even number of
scores or odd number of scores)
Percent Rank (percentile) – calculates the
position of a datapoint in a data set. More
precisely, tells you approximately how many
percent of the data is less than the datapoint.
Range – difference between the maximum
and minimum values in the data set
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Lower quartile – or first quartile, it is the
median of the data values in the lower half of
a data set
Middle quartile – or second quartile, this is
the overall median
Upper quartile – or third quartile, it is the
median of the data values in the upper half of
a data set
Quartiles may help in seeing the variation in a
data set
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For example (bank waiting times):
lower quartile
Big Bank:
median
upper quartile
4.1 5.2 5.6 6.2 6.7 7.2 7.7 7.7 8.5 9.3 11.0
Best Bank: 6.6 6.7 6.7 6.9 7.1 7.2 7.3 7.4 7.7 7.8 7.8
Big Bank range: 11.0 – 4.1 = 6.9
Best Bank range: 7.8 – 6.6 = 1.2
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The five number summary consists of:
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The
The
The
The
The
minimum value
lower quartile (first quartile)
median (second quartile)
upper quartile (third quartile)
maximum value
In SPSS (was called PASW), when viewing
output, first quartile is 25th percentile,
second quartile is 50th percentile, and third
quartile is 75th percentile
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Quartiles are OK for characterizing data, but
standard deviation is preferred by
statisticians
It is a measure of how far data values are
spread around the mean of a data set
Std dev = sqrt(sum of (deviations from the
mean)2 / total number of data values – 1)
Don’t calculate by hand, use SPSS (which we’ll
do in a few minutes)
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A simple way to estimate standard deviation
is the standard deviation estimate
Divide the range by 4
Watch for outliers. They can ruin your range
estimate
What is an outlier? Two or more standard
deviations from the mean (plus OR minus)
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Go back to Big Bank / Best Bank example
Big Bank: range = 6.9
6.9 / 4 = 1.7
Actual standard deviation is 1.96
Best Bank: range = 1.2
1.2 / 4 = 0.3
Actual standard deviation is 0.44
Any outliers? Means are 7.2 and 6.7
Big Bank: 4.1 5.2 5.6 6.2 6.7 7.2 7.7 7.7 8.5 9.3 11.0
Best Bank: 6.6 6.7 6.7 6.9 7.1 7.2 7.3 7.4 7.7 7.8 7.8
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Nice way to view a data set
A histogram is a chart similar to a dotplot
created by defining a set of bins and counting
how many data points lie in each bin. Bars
are drawn with height proportional to the
number of data points in each bin.
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While Excel can do some basic statistics, it is
not considered a serious statistics tool
You really should use something like SPSS or
SAS
We’ll use SPSS since DePaul has a site license
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Copy the dataset Grades.xls from the QRC
website (OlderData) to My Documents and
start SPSS (or try the file IncomeGaps.xls)
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Using SPSS, open the Grades.xls spreadsheet
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Change the variable names and make sure
the data is numeric, not text
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Click on Analyze -> Descriptive Statistics ->
Frequencies
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Be careful! If the numeric fields in the dataset
have any $, % or #, SPSS will have difficulty
converting these to numeric
In particular, if the data has dollar signs, have
SPSS first convert the field to Dollar, then
convert it to Numeric (IncomeGaps.xls)
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Using the grades for Exam 2, find the
◦ 5 number summary (minimum, 1st quartile, median,
3rd quartile, maximum)
◦ Mean
◦ Range
◦ What is the standard deviation?
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Let’s say you have just performed a survey.
One of the questions you ask is, what type of
home computer Internet connection do you
have?
Answers can be: none, dial-up, dsl, cable,
other, not sure.
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Here are some of your results
Respondent ID
11111
11112
11113
11114
11115
11116
Cable Type
no
ds
cm
dk
du
du
Where no = none; ds = dsl; cm = cable modem;
du = dial up; dk = don’t know; ot = other
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You can use SPSS to count the occurrences of
data items, just like a pivot table
Enter your data into SPSS
Click on Analyze / Descriptive Statistics /
Frequencies
Move the variable that you want to count
from the left box to the right box
Make sure Display Frequencies Table is
checked
Run it
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Crosstabs are an extension of pivot tables
Let’s say you have asked a number of
students: How many schools did you apply
to?
You get results something like the following
(in a spreadsheet):
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Respondent ID
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2
3
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Sex
F
M
F
F
M
M
F
F
F
M
Number Schools
2
6
1
4
9
10
3
2
7
5
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Now open the data in SPSS
Then pull down the menu Analyze and click
on Descriptive Statistics, then Crosstabs
What variable do you want in the row? The
column?
When ready, click OK to perform the crosstab.
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Let’s do the activity.
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