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Descriptive Statistics Worksheet using MINITAB 14 How does Store

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Descriptive Statistics Worksheet using MINITAB 14 How does Store Powered By Docstoc
					              Descriptive Statistics Worksheet
                          using MINITAB 14


             How does Store Lighting affect Purchases?

Introduction
The data in this worksheet were recorded on 169 customers at a big supermarket. The
supermarket wanted to see whether the lighting levels in the aisles of the store affected
shopper behaviour. Their detailed objectives were to investigate whether lighting levels
affected the extent to which shoppers examined, handled and selected items on the shelves,
and how long they spent in the aisle.
In this worksheet you will summarise the data, investigating the typical statistics for the
various variables. Descriptive statistics and frequency tables will first be used to investigate
the variables.


Getting started
The data are supplied in Excel format in the file StoreLighting.xls
   •    Start MINITAB and from the main menu select File > Open Worksheet;
   •    in the dialog box that appears choose to view Files of type: Excel (*.xls);
   •    in the Look in box navigate to the folder containing StoreLighting.xls;
   •    click on this file and then Open.

The worksheet contains 14 columns of data:
C1      LIGHT  bright or soft
C2      AGE    Midpoints of 10-20, 20-30, 30-40, 40-50, 50-60, 60-70, 70-80
C3      SEX    m = Male, f = Female
C4-C6   READTOP, READMID, READBOT
               Number of labels read on top, middle or bottom shelf
C7-C9   TOUCHTOP, TOUCHMID, TOUCHBOT
               Number of items touched on top, middle or bottom shelf
C10-C12 HANDTOP, HANDMID, HANDBOT
               Number of items picked up or handled on top, middle or bottom shelf
C13     ITEMS  Number of items put into basket or trolley
C14     TIME   Time spent in aisle (s)


Reading, touching and handling items on different shelves
The numbers of items that shoppers read, touch and/or handle on the top, middle and
bottom shelves are recorded. We shall first look at the descriptive statistics for the numbers
read on each shelf level and compare them.

Descriptive statistics for these variables may be reported in a single table.
   •    From the main menu choose Stat > Basic Statistics > Display Descriptive
        Statistics;
   •    select READTOP, READMID and READBOTT in the Variables: box;
   •    click on OK to obtain the following output.

Descriptive Statistics                                                StoreLighting / MINITAB
                                             1 of 6
Descriptive Statistics: READTOP, READMID, READBOTT

Variable     N   N*     Mean     SE Mean    StDev   Minimum       Q1   Median       Q3
READTOP    169    0   1.2308      0.0908   1.1802    0.0000   0.0000   1.0000   2.0000
READMID    169    0    1.314       0.118    1.528     0.000    0.000    1.000    2.000
READBOTT   169    0   0.0769      0.0252   0.3273    0.0000   0.0000   0.0000   0.0000

Variable   Maximum
READTOP     4.0000
READMID      8.000
READBOTT    2.0000

Q1.    How would you describe the similarities and differences in the number
       of items read from each layer of shelf?
       What does this indicate for the store?
       The mean number of items read from the middle shelf (1.314) is slightly higher than
       that for the top shelf (1.2308) and both of these are much larger than the mean for
       the bottom shelf, (0.0769) which is much less than 1 item on average. The maximum
       numbers of items read varies from 8 for the middle shelf, 4 for the top shelf and only
       2 for the bottom shelf.

       The lower and upper quartiles, and medians are the same for the number of items
       read on the top and middle shelves; all these statistics are 0 for the bottom shelf.

       Hardly anyone reads the labels of items on the bottom shelf, so the store should put
       new items or those it wants to promote on the middle shelf (preferably) or top shelf.

Find the descriptive statistics for the number of items handled on the top, middle and bottom
shelves (HANDTOP, HANDMID and HANDBOT).

Q2.    What differences do you notice?
       On average, shoppers handle about a half of an item on the middle shelf, about a
       quarter on the top shelf and hardly any on the bottom shelf. The maximum numbers
       of items handled is 6 for the middle shelf, 4 for the top and 2 for the bottom. The
       lower and upper quartiles and medians are all 0 for each of the shelf heights.



Investigation for different lighting levels
Here we look at shoppers’ behaviour for the two different lighting levels – bright or soft. For
example, will they read more items if the light is bright?

First we shall tabulate the variable LIGHT to see the numbers of shoppers in each level.
   •   From the main menu choose Stat > Tables > Tally Individual Variables;
   •   select LIGHT in the Variables: box and under Display: tick Counts and Percents;
   •   click on OK to obtain the following output.




Descriptive Statistics                                                 StoreLighting / MINITAB
                                              2 of 6
Tally for Discrete Variables: LIGHT
 LIGHT    Count    Percent
bright       87      51.48
brigth        3       1.78
  soft       79      46.75
    N=      169

Q3.      What does this tell us about the recording of the data?
         Whoever entered the data into the spreadsheet has misspelled “bright” as “brigth” 3
         times.

In order to correct this:
    •    From the main menu choose Data > Code > Text to Text;
    •    select LIGHT in the Code data from columns: and Into columns: boxes;
    •    write brigth in the first Original values: box and bright in the corresponding New:
         box;
    •    click on OK.

Repeat the Tally chart instructions above.

Q4.      What is the breakdown by lighting level?
         Just over half (53%) of the shoppers are in brightly-lit aisles and just under half
         (47%) in softly-lit aisles.

We can also look at the descriptive statistics of items read from the different shelves under
the two lighting levels.

Repeat the instructions above for obtaining Descriptive Statistics, but also
    •    select LIGHT in the By variables(optional): box;

Q5.      Are there any differences in the numbers of items read in bright or soft
         light?
         The mean number of items read on either middle or bottom shelves is greater in
         bright light than soft; however, the mean number read is greater in soft light for the
         top shelf. Otherwise, the statistics are very similar for bright or soft lighting.

Now look at the number of items handled on each shelf level (HANDTOP, HANDMID
HANDBOT) in bright or soft light.

Q6.      Are there any differences in the numbers of items handled in bright or
         soft light?
         The mean number of items handled on the top shelf is greater in soft light than
         bright; the mean numbers handled on either the middle or bottom shelves are about
         the same. In all cases the maximum number of items handled is greater under soft
         light than bright. Otherwise, the statistics are very similar for bright or soft lighting.

Descriptive Statistics                                                     StoreLighting / MINITAB
                                                3 of 6
Number of sales under the two lighting levels
The most important question for the store is whether more items are bought under soft or
bright lights and a good indication of this is the number of items put into a basket or trolley.
We shall now look to see how this compares for the different lighting levels.
      •   From the main menu choose Stat > Tables > Cross Tabulation and Chi-Square;
      •   under Categorical variables: select LIGHT in the For rows: box and ITEMS in the
          For columns: box ;
      •   under Display: tick Counts and Row percents;
      •   click on OK to obtain the following output.

Tabulated statistics: LIGHT, ITEMS

Rows: LIGHT       Columns: ITEMS

                  0        1      All

bright           79      11        90
              87.78   12.22    100.00

soft             73       6        79
              92.41    7.59    100.00

All             152      17       169
              89.94   10.06    100.00

Cell Contents:            Count
                          % of Row

Q7.       Are shoppers more likely to buy under bright or soft lights?
          12% of shoppers under bright lights put 1 item into their trolley or basket, whereas
          only 8% of those under soft lights do. This would indicate that more items would be
          sold if the lighting were bright.

In the same way, look at the proportions of items put into trolleys or baskets by males or
females.

Q8.       Is there any difference in the behaviour of males and females?
          The proportions are almost the same, with about 10% putting 1 item into their trolley
          or basket, whether they are male or female.




Descriptive Statistics                                                 StoreLighting / MINITAB
                                               4 of 6
Comparing the time spent in the aisles under soft and bright light
The store also wanted to know how long shoppers spent in the aisles and whether this was
influenced by the lighting levels. Here, we compare the time spent (TIME) under soft and
bright lights, by first drawing a boxplot.
   •   From the main menu choose Graph > Boxplot;
   •   highlight With Groups under One Y;
   •   click on OK;
   •   select TIME in the Graph variables: box and LIGHT in the Categorical variablesfor
       grouping: box;
   •   under Data View tick the Mean symbol box;
   •   click on OK;
   •   under Labels > Titles/Footnotes write a suitable title for your graph;
   •   click on OK;
   •   click on OK again to produce the following plot.


                            Time spent in the aisles under different lighting levels
                      500



                      400



                      300
               TIME




                      200



                      100



                       0
                                       bright                             soft
                                                        LIGHT



Q9.    What does the boxplot tell you about the times spent in brightly lit or
       softly lit aisles? (Note that you can see the various statistics if you
       hover the mouse over the boxes).
       The mean time spent under soft light is higher than the mean time spent under bright
       light; the medians are almost the same. The inter-quartile range (i.e. the time spent
       by the middle 50% of the shoppers) is less (65s) under soft light than bright light
       (78s). These seem contradictory, so although 50% of shoppers are quicker under
       soft lights, on average they are not.




Descriptive Statistics                                                           StoreLighting / MINITAB
                                                    5 of 6
Q10. What do the asterisks indicate on the boxplot? What would you
     conclude?
        The asterisks indicate that there are “outliers”, i.e. unusually large (in this case) or
        small observations. These can be the result of data collection or entry errors; given
        that we have already seen mistakes in the data entry (brigth for bright) we might
        expect at least some of these to be mistakes. However we have no way here of
        checking.

If we are not sure of the data entry and suspect that large values for TIME may have been
entered in error, we can use a trimmed mean rather than the mean.

Q11. What is a trimmed mean?
        A 5% trimmed mean discards the smallest 5% and largest 5% of values (rounded to
        the nearest integer) and averages the remaining values.

In order to find this and other statistics for time spent under different lighting levels.
    •   From the main menu choose Stat > Basic Statistics > Display Descriptive
        Statistics;
    •   select TIME in the Variables: box and LIGHT in the By variables(optional): box;
    •   under Statistics tick Trimmed mean;
    •   click on OK;
    •   click on OK again to obtain the following output.

Descriptive Statistics: TIME

Variable    LIGHT     N   N*    Mean   SE Mean    TrMean    StDev   Minimum       Q1    Median
TIME        bright   90    0   63.37      5.73     58.09    54.37      8.00    22.00     40.50
            soft     79    0    80.7      10.6      66.2     94.1      10.0     27.0      41.0

Variable    LIGHT        Q3    Maximum
TIME        bright   100.00     210.00
            soft       92.0      482.0

Q12. How do the means and trimmed means compare?
        The mean times spent under soft and bright lights are quite different, being 81s for
        the former and 63s for the latter. However, the trimmed mean values are not so
        different, although that for the soft lighting is still larger, at 66s compared with 58s.



Further investigation
You may want to compare the time spent by males and females (men have a reputation for
being quicker shoppers – is that true?)

Also we have not considered how the lighting affects different age groups – as we get older
our eyesight tends to get worse. Do bright lights help us to shop?



Descriptive Statistics                                                   StoreLighting / MINITAB
                                               6 of 6

				
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Description: Descriptive Statistics Worksheet using MINITAB 14 How does Store