Research - Discussion 8

QUANTITATIVE RESEARCH

METHODOLOGIES

Strategies for Analyzing Quantitative Data

Chapter Eleven

Analyzing the Quantitative Data

 Questions to ask

 What do the data mean?

 What message to the data communicate?

Analyzing the Quantitative Data

 Before employing any statistical procedure consider

how to organize the data set

 Computer spreadsheets are good tools for

organizing data

 Choose the appropriate statistics

Functions of Statistics

 Statistics have two major functions (a) to describe

what the data look like and (b) to allow us to draw

inferences about the data

 Descriptive statistics – describe the data

 Inferential statistics – allow us to draw inferences

Statistics as Estimates of Population

Parameters

 When statistics are used to draw inferences about a population from which a research sample has been drawn, we are using them as estimates of population parameters

 A parameter is a characteristic or quality of a population that, in concept, is a constant; however, its value is variable

 Within the context of quantitative data analysis, a parameter is a particular characteristic of the entire population – which is sometimes called a universe- about which we draw conclusions

 Any calculation we perform for the sample rather than the population is called a statistic

Considering the Nature of the Data

 Consider whether the data

 Have been collected for a single group or, instead, for

two or more groups

 Involve continuous or discrete variables

 Represent nominal, ordinal, interval, or ratio scales

 Reflect a normal or non-normal distribution

Considering the Nature of the Data

 Single-group vs Multi-group data require different

statistical techniques

 A Variable is a quality or characteristic in a

research investigation that has two or more possible

values

 A continuous variable reflects an infinite number of

possible values falling along a particular continuum

 A discrete variable has a finite and small number of

possible values

Considering the Nature of the Data

 Four different scales of measurement

 Nominal Data

 Ordinal Data

 Interval Data

 Ratio Data

Considering the Nature of Data

 Normal and Non-Normal Distributions

 Many theorists have proposed that many characteristics

of living populations reflect a particular pattern that is

called the normal distribution or normal curve or bell

curve

Normal Distribution

Sometimes

called a

normal curve

or a bell

curve

 It is horizontally symmetrical

 Its highest point is at the midpoint – in

statistical terms, three widely used

measures of central tendency – the

mode, the median, and the mean – are

equivalent

 Predictable percentages of the

population lie within any given portion

of the curve

Non-Normal Distribution

Sometimes the

variable

doesn’t fall in

a normal

distribution

 The distribution may be skewed

 It is positively skewed if the peak of the distribution lies to the left of the midpoint

 It is negatively skewed if the peak of the distribution lies to the right of the midpoint

 Kurtosis is an unusually peaked, or pointy, distribution reflecting a leptokurtic curve

 An unusually flat curve is a platykurtic curve

 Percentile ranks form a flat distribution

Choosing Between Parametric and

Nonparametric Statistics

 Parametric statistics are based on certain

assumptions bout the nature of the population in

question

 Two of the most common assumptions are (a) the

data reflect an interval or ration scale and (b) the

data fall in a normal distribution

 Nonparametric statistics are not based on

assumptions

Descriptive Statistics

 Measures of Central Tendency

 This refers to the techniques for finding a point around

which the data revolve

 Three commonly used measures of central tendency are

the mode, the median, and the mean

Measures of Central Tendency

3 measures

Mode

Median

Mean

 Mode is the number that occurs most

frequently

 Median is the numerical center of a set

of data

 Mean is the arithmetic average of the

scores within the data set

Measures of Variability: Dispersion

and Deviation

 The farther the data are dispersed from the central

axis, the greater the margin of error becomes

 To derive meaning from the data it is important to

not only determine their central tendency, but also

their spread – and it helps to explain their spread

in terms of one or more quantitative values

 The simplest measure of variability is the range,

which indicates the spread of the data from lowest

to highest value

Measures of Variability: Dispersion

and Deviation

 The range is easy to compute but has limited usefulness as a measure of variability

 Other measures of variability use the median or mean as a starting point. One measure is the interquartile range which divides the distribution into four equal parts

 Because quartiles are associated with the median, any researcher employing the median as a measure of central tendency should also consider the quartile deviation as a possible statistical measure for variability

Measures of Variability: Dispersion

and Deviation

 If the mean is used as a starting point, then we

calculate the difference between each score and

the mean score – this is called the deviation

 If we add all the differences (ignoring plus and

minus) and then divide the sum by the number of

scores, we get an average of the differences

between any score and the mean. This number is

sometimes called the average deviation (it is a little

used value)

Measures of Variability: Dispersion

and Deviation

 The standard deviation is the measure of variability

most commonly used in statistical procedures

Using the Mean and Standard

Deviation

Raw score

Norm- referenced scores

Percentile rank

Standard score

Standard deviation

Stanine

 Raw score is the number of correct answers on a test

 Norm-referenced scores are scores that reflect where each person is positioned relative to other members of the person’s group

 A percentile rank is an example of a norm- referenced score

 A standard score tells us how far an individual’s performance is from the mean with respect to standard deviation units

 Stanines are a commonly used standard-score scale. They have a mean of 5 and a standard deviation of 2

Measures of Association: Correlation

 Statistical process by which we discover whether

two or more variables are in some way associated

with one another is called correlation

 The resulting statistic is called a correlation

coefficient (a number between negative 1 and

positive 1)

 The most widely used statistic for determining

correlation is the Pearson product moment

correlation

What Correlation Coefficients Tell Us

Direction &

Strength

 Direction (either positive or negative)

 Strength (perfect, strong, weak,

moderate)

How Validity and Reliability Affect

Correlation Coefficients

 Beginning researchers should be aware that the extent to which one finds a statistical correlation between two characteristics depends, in part, on how well those characteristics have been measured

 The researcher will find substantial correlations between two characteristics only if both characteristics are measured with a reasonable degree of validity and reliability

 Remember that correlation does not indicate causation

Inferential Statistics

 Inferential statistics have two main functions

 To estimate a population parameter from a random

sample

 To test statistically based hypotheses

Statistical Techniques for Testing

Hypotheses

These are

some of the

more common

tests

 ANOVA

 ANCOVA

 T-test

 Regression

 SEM

 Mann-Whitney U

 Chi-square

Interpreting the Data

Generalizatio

ns

 Relate the findings to the original research problem and to the specific research questions and hypotheses

 Relate the findings to pre-existing literature, concepts, theories, and research studies

 Determine whether the findings have practical significance as well as statistical significance

 Identifying limitations of the study