SUMMARISING AND PRESENTING DATA

EXPLORING DATA IN TABLES

In this section we will consider ways of presenting data on two or more variables in tables

Example - Number of applicants to UCB
Source: Freedman, Pisani & Purves, "Statistics", Norton 1978.

A table containing the number of applicants for admission to the University of California at Berkley according to gender and major (equivalent to Faculty in Australia) is shown below.

How can you discover and present the main "messages" in the data?

No. of applicants

Major	Men	Women	Total
A	825	108	933
B	560	25	585
C	325	593	918
D	417	375	792
E	191	393	584
F	373	341	714
TOTAL	2691	1835	4526

To compare preferences for major (outcome variables) between men and women (predictor variable) we might calculate the percentage of total admissions by major for each gender (ie column percentages). To do this, multiply each number in the "Men" column by 100/2691 and multiply each number in the "Women" column by 100/1835.

Major	Men	Women
A	31	6
B	21	1
C	12	32
D	15	20
E	7	21
F	14	19
TOTAL	100	99*

*Doesn't add to %100 due to rounding.

Conclusion - men preferred majors A or B, while women preferred majors C, D, E or F.

Dot Chart

You could show the column %s on a bar graph or a dot chart.

To compare gender distributions (outcome) for majors (predictor), calculate % of men and women for each major (ie row percentages)

Major	Men	Women	Total
A	88	12	100
B	96	4	100
C	35	65	100
D	53	47	100
E	33	67	100
F	52	48	100

Conclusion - Majors A and B were predominantly men, C and E were predominantly women, and majors D and F were approximately balanced between men and women.

Example - Newcastle restaurant survey

The variable OWNER takes 3 values :

1. sole proprietorship
2. partnership,
3. corporation.

1. fewer than 5 employees
2. between 5 to 20 employees
3. more than 20 employees

For example, the first restaurant in the data set was owned by a corporation (code 3) and had more than 20 employees (code 3).

The data were entered into a MINITAB worksheet by the following commands:

MTB> read c1 c2
DATA> 3 3
DATA> 1 2
DATA> 1 1
DATA> 3 1
....
....
....
DATA> end
     20 ROWS READ
MTB> name c1 'owner' c2 'size'

The command TABLE C1 C2 will result in a table in which the rows are OWNER, the columns are SIZE and the numbers in the cells of the table are the counts (frequencies).

A table is often easier to interpret if the counts are converted to percentages.

The subcommand COLPERCENT calculates column percentages and the subcommand ROWPERCENT calculates row percentages.

MTB> table c1 c2

 ROWS: owner     COLUMNS: size

           1        2        3      ALL
 
  1        3        4        0        7
  2        2        0        1        3
  3        4        3        3       10
 ALL       9        7        4       20

  CELL CONTENTS --
                  COUNT

MTB> table c1 c2;
SUBC> colpercent.
 
 ROWS: owner     COLUMNS: size

           1        2        3      ALL
 
  1    33.33    57.14      --     35.00
  2    22.22      --     25.00    15.00
  3    44.44    42.86    75.00    50.00
 ALL  100.00   100.00   100.00   100.00

  CELL CONTENTS --
                  % OF COL

MTB> table c1 c2;
SUBC> rowpercent.
 
 ROWS: owner     COLUMNS: size

           1        2        3      ALL
 
  1    42.86    57.14      --    100.00
  2    66.67      --     33.33   100.00
  3    40.00    30.00    30.00   100.00
 ALL   45.00    35.00    20.00   100.00

  CELL CONTENTS --
                  % OF ROW

Which category of OWNER had the highest frequency? What percentage of all OWNER were in that category? Which category of SIZE had the highest frequency?

Contingency Tables

Example - Number of deaths in Australia (1989)

The table below shows the numbers of deaths in Australia in 1995 for people aged 15-24 years (Source: Australian Bureau of Statistics, 3303.0, pp.33-35):

Cause of death	Males	Females	Total
Motor vehicle accident
448	146	594
Suicide	350	84	434
Other accident	257	74	331
Malignant cancer	86	50	136
Other diseases	267	153	420
Total	1,408	507	1,915

Each person who died was categorised by sex (M or F) and by cause of death. A cross-classified table is sometimes called a contingency table.

Do males and females in this age group die from the same causes?

To compare patterns of cause of death you need to consider relative frequencies or percentages because the total numbers of deaths are not the same for males and females.

Marginal frequency distribution for Deaths By Gender

	Males	Females	Totals
Numbers	1408	507	1915
Relative Frequency	0.74	0.26	1.00

(e.g. 1408/1915 is approximately 0.74)

Conclusion - In this age group there are about 3 times more male deaths than female deaths.

Marginal frequency distribution for Cause of Death

Cause	Number	Relative frequency
Motor vehicle accident	594	0.31
Suicide	434	0.23
Other accidents	331	0.17
Malignant neoplasms	136	0.07
Other diseases	420	0.22
Total	1915	1.00

This table is obtained by collapsing the original table over the factor 'sex'. Conclusion - The main causes of death in this age group are motor vehicle accidents, which cause 31% of all deaths, and suicides, which account for 23%.

Conditional frequency distribution

	Males		Females
Cause	No.	%	No.	%
Motor vehicle accidents	448	32	146	29
Suicide	350	25	84	17
Other accidents	257	18	74	15
Cancer	86	6	50	10
Other diseases	267	19	153	30
Total	1408	100%	507	100%

Conclusion - Motor vehicle accidents were the major cause of death for both males and females in the age group 15-24 years, accounting for about 30% of deaths. Suicides were more common for males than for females.

The need to consider group size

Example - Infant deaths in 1989

Area	Neonatal deaths	Live births	Total births	Death rate (%)
Lake Macquarie	24	2304	2328	1.03
Newcastle	26	1835	1861	1.40
Maitland	5	814	819	0.61
Cessnock	7	725	732	0.96
Port Stephens	10	631	641	1.56
Muswellbrook	2	295	297	0.67

Source: Hunter Health Statistics Unit

You cannot directly compare the numbers of deaths in each area because these depend on the number of births. You need to convert the numbers of deaths to death rates:

Rules for presentation of tables

• Two examples demonstrating patterns and exceptions.
• An article by Ehrenberg on designing readable tables.