STATISTICS AND MEASUREMENTSOVERVIEW: NATURE OF DATA

STATISTICS

SPECIFIC NUMBERS: numerical measurement determined by a set

of data

METHOD OF ANALYSIS: a collection of methods for planning

(quantitative research), obtaining data, and then then organizing,

summarizing, presenting, analyzing, interpreting, and drawing

conclusions based on the data

STATISTICS

Specific number - numerical measurement determined by a set of data

Example: Seventy-seven percent (77%)f people surveyed believed that learning statistics is easy and fun.

The new Miss Universe has the following vital statistics: 34-24-34.

STATISTICS

Method of analysis : a collection of methods for

(1) planning experiments,

(2) obtaining data, and then

(3) organizing,

(4) summarizing,

(5) presenting,

(6) analyzing,

(7) interpreting, and

(8) drawing conclusions based on the data

Two Broad Areas

STATISTICS

(Collection, Organization, Summary,

Presentation, Analysis and

Interpretation of Data)

DESCRIPTIVE

-deals with processing data without attempting to draw any inferences/conclusions from them.

-It refers to the representation of data in the form of tables, graphs and to the description of some

characteristics of the data, such as averages and deviations.

INFERENTIAL

-is a scientific discipline concerned with developing and using mathematical tools to make

estimates/projections and inferences/conclusions.

THE NATURE OF DATA(LEVELS OF)MEASUREMENT

DEFINITIONS

DATA

QUALITATIVE

(CATEGORICAL)

OR

(ATTRIBUTE)

consist of attributes, labels, or non-numerical entries

QUANTITATIVE

(NUMERICAL)

consist of numerical measurements or counts

Classifying Data by Type

The suggested retail prices of several Ford vehicles are shown in the table. Which data are qualitative data and which are quantitative data?

Model Suggested Retail Price

Focus SedanFusionMustangEdgeFlexEscape HybridExpeditionF-450

$15,995$19,270$20,995$26,920$28,495$32,260$35,085$44,145

Classifying Data by Type

The information shown in the table can be separated into two data sets. One data set contains the names of vehicle models, and the other contains the suggested retail prices of vehicle models.

Model Suggested Retail Price

Focus SedanFusionMustangEdgeFlexEscape HybridExpeditionF-450

$15,995$19,270$20,995$26,920$28,495$32,260$35,085$44,145

The suggested retail prices are numerical entries, so these are quantitative data.

The names are non-numerical entries, so these are qualitative data.

Classifying Data by TypeThe populations of several regions in Thailand are shown in the table. Which data are qualitative data and which are quantitative data? (Source: http://www.citypopulation.de/Thailand-Cities.html) Identify the two data sets. Decide whether each data set consists of numerical or non-numerical entries. Specify the qualitative data and the quantitative data.

Name Population (2010)

Bangkok (and Vicinities)EasternNortheasternNorthernSouthernSub-centralWestern

14,565,5465,163,86818,808,01211,432,4888,841,3643,109,5313,558,644

Levels of Measurements Another common way of classifying data is to use

four levels of measurement: nominal, ordinal, interval, and ratio.

In applying statistics to real problems, the level of measurement of the data is an important factor in determining which procedure to use.

Never do computations and never use statistical methods with data that are NOT appropriate.

TYPES OF DATA

Qualitative

Categorical or Attribute data

can be separated into different categories that are distinguished by some nonnumeric characteristic

NOMINAL

ORDINAL

Quantitative

Consist of numbers representing counts or measurements

INTERVAL

RATIO

DEFINITIONS

Data at the nominal level of measurement are qualitative only which are categorized using names, labels, or qualities.

The data cannot be arranged in an ordering or ranking scheme (like low to high).

No mathematical computations can be made at this level.

Example: Gender: male or female (2 levels)

Survey responses: yes, no, undecided (3 levels)

Marital Status: Single, Married, Divorced (3 levels)

Type of Residence: Owned, Rented, Living with Relatives

DEFINITIONS

Data at the ordinal level of measurement are mostly qualitative.

Data at this level can be arranged in order or ranked, but differences between data entries are not meaningful.

Examples: Course grades A, B, C, D, F (5 levels)

Survey Responses: Always, Oftentimes, Sometimes, Seldom,

or Never (5 levels)

Year Level: Freshman, Sophomore, Junior, Senior (4Levels)

Educational Attainment: Elementary, High School, College

(3 levels)

The two highest levels of measurement consist of quantitative data only.

Data at the interval level of measurement can be ordered, and meaningful differences between data entries can be calculated.

At the interval level, division between data entries can be calculated but has no important meaning.

At the interval level, a zero entry simply represents a position on a scale; the entry is not a natural or inherent zero.

interval level of measurement

Calendar Years: 1850, 1998, 1776, and 2014

1. Category: [19th , 20th , 18th , 21st Centuries]

2. Rank/Order: [1776, 1850, 1998, 2014]

3. Difference between two values can be calculated: 1998 2014 = 16

(year 1998 is 16 years earlier than year 2014)

2014 1850 = 164

(year 2014 is 164 years later than year 1850)

interval level of measurement

Number Grades: 75, 88, 94, 90, 85

1. Category: (75-80), (81-85), (86-90), (9195)

2. Rank/Order: 75, 85, 88, 90, 94

3. Difference between two values can be calculated: 85 88 = 3

(85 as a grade is 3 points lower than 88 as a grade)

94 90 = 4

(95 as a grade is 4 points higher than 90 as a grade)

Interval Data

Example: IQ score

1. Category2. Rank3. Difference between 2

values can be calculated4. No inherent zero (Zero

is not a starting point)

Data at the ratio level of measurement are similar to data at the interval level, with the added property that a zero entry is an inherent or natural zero.

A ratio of two data values can be formed (division between two data entries) so that one data value can be meaningfully expressed as a multiple of another.

DEFINITIONS: Ratio

Example: Prices of college textbooks in US dollars: $25, $150, $200

1. Category: ($1 - $99), ($100 - $199), ($200 - $299)

2. Rank/Order: $25, $150, $200

3. Difference between two values:

$25 $150 = - $125 (a $25 book is $125 cheaper than a $150 book)

$200 $150 = $50 (a $200 book is $50 more expensive than a $150

book)

4. Inherent Zero (Zero as starting point)

$150 $25 = 6

A $150 book is 6 times more expensive than a $25 book or

A $25 book is 6 times cheaper than a $150 book

DEFINITIONS: Ratio Example: Examination Scores (100 points): 70, 88, 45, 55, 72

1. Category: (0 25), (26 50), (51 75), (76 100)

2. Rank/Order: 45, 55, 70, 72, 88

3. Difference between two values

70 45 = 25

(A score of 70 is 25 points more than a score of 45)

55 88 = 33

(A score of 55 is 33 points lower than a score of 88)

4. Inherent Zero (Zero as starting point)

88 45 = 1.96

A score of 88 is about 1.96 times higher than a score of 45 or

A score of 45 is about 1.96 times lower than a score of 88

The following tables summarize which operations are meaningful at each of the four levels of measurement. When identifying a data sets level of measurement, use the highest level that applies.

Level of Measurement

Put data in Categories

Arrange data in order

Subtract data values

Inherent/Natural Zero

NominalOrdinalIntervalRatio

YESYESYESYES

NOYESYESYES

NONOYESYES

NONONOYES

DEFINITIONS

Population (N): the complete collection of all elements (scores, people, measurements, and so on) to be studied. The collection is complete that it includes all subjects to be studied.

Population

Study Unit

Target Population

The whole group of study units which we are interested in applying our inferences or

conclusions

Study Population (Sample)

The group of study units to which we can legitimately apply our inferences or

conclusions

DEFINITIONS

DEFINITIONS

The whole pizza represents a POPULATION.

The slice of a pizza represents a SAMPLE (Study Population)

DEFINITIONS

The whole pizza represents a POPULATION.

The slice of a pizza represents a SAMPLE (Study Population)

DEFINITIONS

Example: A fisheries researcher is interested in the behaviour pattern of a crab along the coast of the Gulf of Siam. It would be impossible to investigate every crab individually. The only way to make any kind of educated guess about their behaviour would be by examining a small sub-collection, that is, a sample.

DEFINITIONS

Example: Suppose a machine has produced

10,000 electric bulbs and we are interested in

getting some idea about how long the bulbs will

last. It would not be practical to test all the bulbs

so just select randomly 50 of these bulbs to test.

The 10,000 bulbs constitute the population and

the 50 bulbs a sample.

END OF SESSION