CHAPTER 1 Collecting Data

8/10/2019 CHAPTER 1 Collecting Data

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MISS FARAH DAYANA

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LEARNING OUTCOMESAt the end of this lecture, students should be able to;

To understand the process of data collection.

To understand the various types of data and variables

To demonstrate ways to organize data using FrequencyDistributions.

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IntroductionStatistics is a field of study concerned with

Collection, organization, summarization, and

analysis of data

Drawing inferences about a body of data when

only a part of the data is observed.

Biostatistics is the application of statistics to a wide

range of topics in biology.

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Data: The raw material of statistics is data.

We may define data as figures. Figures results from theprocess of countingor taking a measurement.

For example:

- When a hospital administrator counts the number ofpatients (Counting)

- When a nurse weighs a patient (Measurement)

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Sources of Data1. Routinely kept records

For an example: Hospital medical records containimmense amounts of information on patients

2. External recordsThe data needed to answer a question may already exist

in the form of published reports or researchliterature etc.

For an example: Number of mortality by dengue fever in2012

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3. Surveys

The sources may be a survey, if the data needed is aboutanswering certain questions.

4. ExperimentsFrequently the data needed to answer a question are

available only as the result of an experiment.

For an example:

If a researcher wishes to know how effective a drug is as atreatment of cancer

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Collecting data

Data can be collected using a questionnaireor a data collection sheet.

A questionnaireis used when you wish to ask a sample of

people a series of structured questions relevant to your line of

enquiry.

A data collection sheetor observation sheet is used when

recording results involving counting, measuring or observing. It

can also be used to collect the answers to a few simple questions.

Data can also be collected from secondary sourcessuch as the Internet,

newspapers or reference books.


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Designing a questionnaire

A better question would be:

How much of the Olympics coverage did you watch?

Tick one box only.

None

Less than 1 hour a day

Between 1 to 2 hours a day

More than 2 hours a day

Every eventuality has been accounted for and the person answering the

question cannot give another choice.


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How would you rate the leisure facilities available in your local area? Tick one

box only.

Designing a questionnaire

A scale can be used when asking for an opinion.

For example,

Excellent UnsatisfactoryPoorSatisfactoryGood


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Designing a data collection sheet

A data collection sheet can be used to record data that comes from counting,

observing or measuring.

It can also be used to record responses to specific questions.

For example, to investigate a claim that the amount of TV watched has an impact

on weight we can use the following:

age gender height (cm) weight (kg) hours of TV watched per week


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Using a tally chart

When collecting data that involves counting something we often use a tally chart.

For example, this tally chart can be used to record peoples favourite snacks.

favourite snack tally frequencycrisps

fruit

nuts

sweets

The tally marks are recorded, as responses are collected,

and the frequencies are then filled in.

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VariableWhen collecting or gathering data we collect data

from individuals cases on particular variables. A variable is a unit of data collection whose value

can vary. It is a characteristic that takes on different values For an example:- Heart rate- The heights of adult males- The weights of preschool children- The ages of patients

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Types of Variable

Quantitative Qualitative

It can be measure

For example:-heights-weights-ages

Many characteristics are notcapable of being measured.Some of them can be ordered orranked.

For example:-Race-Social Class


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Categorical dataCategoricaldata is data that is non-numerical.

For example,

Sometimes categorical data can contain numbers.

For example,

favourite football team,

eye colour,

birth place.

favourite number,

last digit in your telephone number,

most used bus route.


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Discrete and continuous data

Discretedata can only take certain values.

Continuousdata comes from measuring and can take any value within a

given range.

Numerical data can be discreteor continuous.

For example,

For example,

shoe sizes,

the number of children in a class,

the number of sweets in a packet.

the weight of a banana,

the time it takes for pupils to get to school,

the height of 13 year-olds.


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There are four types of data or levels ofmeasurement:

1. Nominal 2. Ordinal

3. Interval 4. Ratio


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Nominal or categorical data is data that comprises of categoriesthat cannotbe rank ordered each category is just different.

The categories available cannot be placed in any order and no

judgement can be made about the relative size or distance fromone category to another.

Nominal data


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Examples:

Nominal data

What is yourgender? (please tick)

Male

Female

Did you enjoy thefilm? (please tick)

Yes

No


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Ordinal data is data that comprises of categories that canberank ordered.

Similarly with nominal data the distance between each

category cannot be calculated but the categories can beranked above or below each other.

Ordinal data


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Example:

Ordinal data

How satisfied are you with the levelof service you have received? (pleasetick)

Very satisfied

Somewhat satisfied

Neutral

Somewhat dissatisfiedVery dissatisfied


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Both interval and ratio data are examples of scale data.

Scale data:

data is in numeric format (50, 100, 150)

data that can be measured on a continuous scale

the distance between each can be observed and as a

result measuredthe data can be placed in rank order.

Interval and ratio data


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Interval data measured on a continuousscale and has notrue zero point.

Examples:

Time moves along a continuous measure or seconds,minutes and so on and is without a zero point of time.

Temperature moves along a continuous measure ofdegrees and is without a true zero.

Interval data


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Ratio data measured on a continuousscale and doeshavea true zero point.

Examples:

Age

Weight

Height

Ratio data


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Population The entire pool from which a statistical sample is drawn

For an example: The weights of all the children enrolled in

a certain elementary school.

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Sample

A data sample is a set of data collected and/orselected from a statistical population

For an example: The weights of children in Class A and

B of that elementary school


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Frequency DistributionsAfter collecting data, we need to organize

and simplify the data so that it is possible toget a general overview of the results.

One method for simplifying and organizingdata is to construct a frequencydistribution.


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Frequency Distributions (cont.)A frequency distributionis an

organized tabulation showing exactlyhow many individuals are located ineach category on the scale ofmeasurement


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Frequency Distribution TablesA frequency distribution tableconsists of at

least two columns - one listing categories on thescale of measurement (X) and another forfrequency (f).

In the X column, values are listed from the highestto lowest, without skipping any. The sum of the frequencies should equal N.


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A third column can be used for the proportion (p) orrelative frequency for each category: p = f/N. The sumof the p column should equal 1.00.

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Frequency Table

A research study has been conducted

examining the number of children in the

families living in a community. The

following data has been collected based ona random sample of n = 30 families from

the community.

2, 2, 5, 3, 0, 1, 3, 2, 3, 4, 1, 3, 4, 5, 7, 3, 2, 4,1, 0, 5, 8, 6, 5, 4 , 2, 4, 4, 7, 6

Organize this data in a Frequency Table! 30


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X=No. of

Children

Count

(Frequency)

Relative Freq.

0 2 2/30=0.067

1 3 3/30=0.100

2 5 5/30=0.167

3 5 5/30=0.167

4 6 6/30=0.200

5 4 4/30=0.133

6 2 2/30=0.0677 2 2/30=0.067

8 1 1/30=0.033

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G d F


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Grouped Frequency

Distribution Sometimes, however, a set of scores covers a wide

range of values. In these situations, a list of all the Xvalues would be quite long - too long to be a simplepresentation of the data.

To remedy this situation, a grouped frequencydistributiontable is used.


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Grouped Frequency Distribution (cont.) In a grouped table, the X column lists groups of

scores, called class intervals, rather thanindividual values.

These intervals all have the same width, usually asimple number such as 2, 5, 10, and so on.


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Chapter 2 34

Grouping dataTips for grouping data

Tips for grouping lots of data

Choose interval widths that reduce your data to 5 to 10intervals.

5 10 15 20 25 30 35


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Chapter 2 35


Choose meaningful intervals.

Which is easier to understand at a glance?

5 10 15 20 25 30 35

4 7 10 13 16 19 22

or


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Chapter 2 36


Interval widths must be the same.

5 10 15 20 25 30 35

5 10 20 22 30 33 35

NOT


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Chapter 2 37


Intervals cannot overlap.

5-10 11-15 16-20 21-25 26-30 31-35 36-40

5-10 10-15 14-20 20-26 25-30 30-35 35

NOT


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Chapter 2 38

Grouping dataAn example


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Chapter 2 39

Grouping dataAn example


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Chapter 2 40

Cumulative Frequency Distribution Cumulative frequency distribution

Shows how many cases (data points) have been

accounted for out of the total number of cases (datapoints).


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Chapter 2 41

Cumulative Frequency Distribution

How many data points have accounted for as eachgroup is displayed.


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Chapter 2 42

Cumulative Frequency Distribution

Cumulative frequencies can also be illustratedusing percentages.


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Cumulative Relative Frequency

- the sum of the relative frequencies for all values at or belowthe given value expressed as a proportion;

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MathAnxietyScores Freq

RelativeFreq

CumulativeFreq

CumulativeRelative Freq

1 1 0.05 1 0.052 2 0.09 3 0.14

3 3 0.14 6 0.28

4 4 0.18 10 0.465 5 0.23 15 0.69

6 0 0 15 0.69

7 2 0.09 17 0.78

8 3 0.14 20 0.92

9 1 0.05 21 0.97

10 1 0.05 22 1.02


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Laws Covering Sales of Firearms: Increase

Restrictions( 2000)?

More Less Same No opinion

Men(N=493) 256 39 193 5Women(N=538) 387 11 129 11


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Men and Firearm Restrictions: Frequency

Distribution(N=493)

F CF RF CRF

More 256 256 .52 .52

Less 39 295 .08 .60

Same 193 488 .39 .99No opinion 5 493 .01 1


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Example

These data represent the record high temperatures for

each of the 50 states. Construct a grouped frequencydistribution for the data using 7 classes.

112 100 127 120 134 118 105 110 109 112

110 118 117 116 118 122 114 114 105 109

107 112 114 115 118 117 118 122 106 110116 108 110 121 113 120 119 111 104 111

120 113 120 117 105 110 118 112 114 114


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Class limits

Classboundaries Frequency

Relativefrequency

Cumulativefrequency

100-104 99.5-104.5 2 0.04 2

105-109 104.5-109.5 8 0.16 10

110-114 109.5-114.5 18 0.36 28

115-119 114.5-119.5 13 0.26 41

120-124 119.5-124.5 7 0.14 48

125-129 124.5-129.5 1 0.02 49

130-134 129.5-134.5 1 0.02 50


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THANK YOU!

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CHAPTER 1 Collecting Data