Statistics

Yikes!

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?

Statistics that help to summarizeFrequenciesMeasures of central tendency

ModeMedianMean

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

An example of data analysis

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?

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

The bodyReport on the data analysisUse statistics and graphs to answer the objectives for the paper

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.

Your implicationsBe helpful to the creativeRemember, you are developing an advertising solution, not a marketing solution.