Why do we use statisticsSummarize large numbers of responses
Remember the focus group?
To make comparisonsDo men like RC better, or do women?
To examine relationshipsAre greater amounts of advertising associated with higher sales?
ModeThe most frequently occurring responseWhat is the mode for this sample?
Male, Male, Female, Male, Female, Male
How about this sample?A, B+, A, C, D
And this one?100, 98, 94, 94, 88, 86, 86, 84, 80
ModeMode=Male
Male, Male, Female, Male, Female, Male
Mode=AA, B+, A, C, D
Mode=94 and 86100, 98, 94, 94, 88, 86, 86, 84, 80
What levels of measurement are these scales?
ModeStrengths:
Can be used with any level of measurementEasy to calculate and understand
Bad points:Can be wildly inaccurate as an “average”There can be many modes, or none at all.
MedianThe point on a measure where half of the responses are above and half are below.Requires that observations can be ranked
SampleA
C+B-DB
Sample (ranked) A
BThe median B-
C+D
MedianWhich observation is the middle one?If you have an odd number of observations (n), then the middle observation (after ranking) is (n+1)/2. Odd # 1, 4, 6 Observe n = 3. (3+1)/2 = 4/2 = 2 = 2nd observation4 is the second observationMedian = 4
MedianWhich observation is the middle one?# observations is even, then you average the two middle observations: (n/2) and (n/2)+12, 4, 6, 8(n/2) = (4/2) = 2 = second observation(n/2) + 1 = 2+1 = 3 = third observationAverage of 4 (2nd obs) and 6 (third obs) is 5Median is 5
MedianGood points
Usable with any level of measurement except nominal
Much better “average” than mode
Good and bad point:Not sensitive to extremes or to size of scale intervals
Sample 1: 1, 2, 4, 7, 10Sample 2: 1, 2, 4, 7, 10 million
MeanMost common measure of “average”Usable only with interval or ratio measuresTo get a mean: sum the observations, then divide by the number of observations (n).Obs: 2,4,3,1,8,0 Sum: 2+4+3+1+8+0=18Divide by n n=6 18/6= 3 The median?2.5
MeanGood Points:
Commonly used and understood
Sensitive to scale intervalsBad Points:
Cannot be used with nominal or ordinal dataCan be distorted by extreme observations
Getting information from surveysSPSS is a statistical program
Excel on steroids
Set up like a spreadsheet
Frequencies printout in SPSS
How interested in participating?
14 4.2 4.2 4.2
15 4.5 4.5 8.7
17 5.1 5.1 13.7
27 8.0 8.1 21.8
45 13.4 13.4 35.2
48 14.3 14.3 49.6
169 50.3 50.4 100.0
335 99.7 100.0
1 .3
336 100.0
Not interested
2.00
3.00
4.00
5.00
6.00
Very interested
Total
Valid
SystemMissing
Total
Frequency Percent Valid PercentCumulative
Percent
How interested are you in participating in a study abroad program while at UF?
Values
Frequency of occurrencePercent of occurrence
Frequencies printout in SPSS
How interested in participating?
14 4.2 4.2 4.2
15 4.5 4.5 8.7
17 5.1 5.1 13.7
27 8.0 8.1 21.8
45 13.4 13.4 35.2
48 14.3 14.3 49.6
169 50.3 50.4 100.0
335 99.7 100.0
1 .3
336 100.0
Not interested
2.00
3.00
4.00
5.00
6.00
Very interested
Total
Valid
SystemMissing
Total
Frequency Percent Valid PercentCumulative
Percent
How interested are you in participating in a study abroad program while at UF?
Percentages w/o missing valuesSums the percentages
Frequencies printout in SPSSHow interested are you in participating in a study abroad program while at UF?
Frequencies printout in SPSSHow interested are you in participating in a study abroad program while at UF?
Statistics
How interested in participating?335
1
5.6687
7.0000
7.00
Valid
Missing
N
Mean
Median
Mode
How do we use this output?Use frequencies to get a mean for each dimension:
Low price: M = 4.67Safety: M = 3.92Fuel efficiency: M = 2.91Reliability M = 4.85
How do we use this output?
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
L Price Safety Fuel E Reliab
Problems with the output?
How do we use this output?
1
1.5
2
2.5
3
3.5
4
4.5
5
L Price Safety Fuel E Reliab
Figure 1: Average importance ratings for car attributes
Scale: 1=Not important, 5=Very important
Answering objective 1Fact:
Car buyers are most interested in reliability and low price
Implication:Jetta is well-positioned to compete on reliability. The target audience should be given facts to support this: our warranty, our JD Power reliability award, our excellent review from Consumer Reports, etc.Although the Jetta is not a low price car, it is average for its class
1
1.5
2
2.5
3
3.5
4
4.5
5
L Price Safety Fuel E Reliab
Answering objectives 1,2, & 3Can be done using the frequencies command if you request item meansNote: you do not need to report the actual frequencies in the report, just the appendix
What do you do in your reportTitle page, Exec Summ, Intro (Objectives+method)Body (Subheads organized by objectives)
What you found (describe statistically)What it means (your analysis)
Overall conclusionsPrintouts in appendix
Figure 1: Preferred Cola
Percent Preferring
0
5
10
15
20
25
30
35
40
45
Percent responses to “My preferred brand of colas is:”
CokePepsi RC
Figure 2: Cola preference by Gender
05
101520253035404550
Men Women
Coke
Pepsi
RC
Percent within each gender group responding to “My preferred brand of colas is:”
ImplicationsOur data suggest two important themes: first, Coke is the brand preferred most overall, second, men show a greater preference for Coke than do women. In our view, this reinforces the need to more aggressively position Coke as a beverage for women cola drinkers.