Quantitative Analysis: Basics Sebastian M. Rasinger Quantitative Research in Linguistics. An...

Quantitative Analysis: Basics

Sebastian M. RasingerQuantitative Research in

Linguistics. An Introduction2nd edition. 2013.

London: Bloomsbury

S.M.Rasinger. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.

Agenda

• Statistics – what for?• Quantitative data – what, how, why?• Descriptive statistics

– frequencies– Measures of location– Measures of dispersion

• Relationships between variables


What is statistics?

• Any orderly summary of numbers, e.g. results of an election, league table etc

• Numerical measurement describing some characteristic of a sample

• Collection of methodological tools which help to systematically and exemplarily collect, process and display information, e.g. inflation rate, unemployment rate


Statistics as a basis for decisions

• Numerous possibilities to process an issue statistically problem of measurement

• Different interpretation of results: glass half empty or half full?

• Manipulation of raw data


Statistics: 3 purposes

• Description: – Quantifying and summarising information in

order to describe and display an issue in the most effective and optimal manner: tables, graphs, main statistical values

– Aim: describing the reality


Statistics: 3 purposes (cont’d)

• Generalisation:– Inference: inferring information about the

population via a small sample

Population sample


Statistics: 3 purposes (cont’d)

• Identification of causal relationships, i.e. how two (or more) phenomena are related

• e.g. effect of learner’s age on language attainment


Quant. Data: discrete or continuous

• Discrete: finite or countable number of possible values– E.g. numbers of students in a class (there’re no half

students…)

• Continuous: infinitely many possible values on a continuous scale without gaps/interruptions– E.g. amount of coffee a university lecturer drinks a

day: continuous (e.g. 1.256 litres)


Levels of measurement

• Nominal data: – names, labels, categories. Cannot be

arranged in high/low scheme, e.g. sex• Ordinal data:

– Data may be arranged in some order, but differences between value cannot be determined or are meaningless,

– e.g. ‘good’ – ‘average’ – ‘poor’ rankings


Levels of measurement (2)

• Interval data:– meaningful difference between data, but no

natural zero starting point for when no quantity is present, e.g. Fahrenheit: 0° doesn’t mean no heat

• Ratio data:– Natural zero point, e.g. length of lecture in

minutes: 0 minutes = no lecture


Absolute and Relative frequency

• Students on a year 1 UG course achieved the following results in an exam

1st class 4

Upper Second Class 8

Lower Second Class 11

Third Class 3

Fail 1

Absolute frequency


Absolute & Relative frequency (2)

• Relative frequency:

n

classoffrequencyclassaoffrequencyrelative

Where n is the total number of items/observations in a sample

1481.0274 classaoffrequencyrelative


Relative frequencyAbs. Rel. %

1st class 4 0.1481 14.81

Upper Second Class 8 0.2963 29.63

Lower Second Class 11 0.4074 40.74

Third Class 3 0.1111 11.11

fail 1 0.037 3.7

27 1 100

Percentage: relative frequency x 100S.M.Rasinger. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.

Summarizing data: classes and class width

• The following table shows the number of students for 20 courses over the last year

No obvious classes. Useless information.1. Determine number of non-overlapping

classes2. Determine the width of each class3. Determine the class limits

12 14 19 18 15 15 18 17 20 27

22 23 22 21 33 28 14 18 16 13


Classes and class width1. 20 observations 5 classes reasonable2. Width of classes

3. Class limits• Lower limit: smallest possible value in a class• Upper limit: largest possible value in a class

• Number of classes, width and limits depend on researcher’s judgement

classesofnumbervaluedatasmallestvaluedatalaregstwidthclassapprox .


Classes and class width (cont’d)

52.451233

classesofnumbervaluedatasmallestvaluedatalaregstwidthclass

Class intervals Frequency Relative frequency10-14 4 0.2015-19 8 0.4020-24 5 0.2525-29 2 0.1030-34 1 0.05

Total 20 1


Cumulative frequencies

• Running total of frequencies through all classes

Class intervals f Rf cf cRf10-14 4 0.20 4 0.2015-19 8 0.40 12 0.6020-24 5 0.25 17 0.8525-29 2 0.10 19 0.9530-34 1 0.05 20 1

Total 20 1


Quantitative Analysis: Basics Sebastian M. Rasinger Quantitative Research in Linguistics. An...

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