# Introduction & Descriptive Statistics

**Topics:**Standard deviation, Level of measurement, Median

**Pages:**9 (1341 words)

**Published:**August 17, 2010

INTRODUCTION & DESCRIPTIVE STATISTICS

BASIC CONCEPTS

Situation: A journalist is preparing a program segment on what appears to be the relatively disadvantaged financial position of women and the incidence of female poverty in Australia.

Several questions may arise, for example:

• What is the pattern of female incomes?

• How severe is the problem of female poverty and what proportion fall below the ‘poverty line’? • Has their general level of income improved over the last ten years? • Are single working mothers especially disadvantaged? • Working mothers often need to put their children into day-care. What should the capacity of the local centre be? • How does their income compare with their male counterparts? Has the gap become any smaller over the last ten years? • Do women have less leisure time than their married partners? • Has the occupational pattern of women changed since the previous generation? • Is there any connection between the occupation of a working mother and the leisure activities of her eldest daughter? • Are their incomes related to age, ethnic origin, education or other factors?

Answering these questions would require almost the full range of techniques covered in this course. One of the most important initial steps in this investigation process is to develop a realistic picture of how the incomes of adult females and other variables of interest in the study vary. All investigation and research is about Variables. In this instance,

The Variables of interest in the study include

E.g.

Population: The whole or entire collection of cases that are of interest in an investigation. Eg.

Sample: A part of that population which is small enough to be economical and large enough to give us a reasonably accurate picture of the whole. Eg.

Data: The measured values of the variable(s) of interest for every member of the sample. Eg.

Statistic: A summary measure of the variable of interest in the sample. Eg.

Parameter: A summary measure of the variable of interest in the population Eg.

Government social security policy should be based on the proportion of all women who live below the poverty line.

However, this proportion is a parameter, which can be guessed, theorised, assumed, believed or estimated, but almost never known for certain. We must use sample statistics to assist us in learning about them.

Statistical Inference

• In general, we never see the WHOLE (population) but must make our decision based on information gathered from the PART (sample). Whenever we draw conclusions about the whole population based on sample information, we are practising STATISTICAL INFERENCE.

Eg.

• Inferences and conclusions can always be wrong. There can never be complete certainty. Later we will apply the concepts of Confidence and Significance to statistical inference. Crudely speaking,

• Confidence level is concerned with our chances of being right.

• Significance level is concerned with our chances of being wrong. TYPE OF VARIABLES & LEVELS OF MEASUREMENT

Nominal = Categorical = Qualitative

Eg.

• The categories may be recorded in number form (eg 1,2,3,4) but the numbers have no numerical meaning and generally cannot be used in calculation.

Ordinal = Ranked

Eg.

• Order is meaningful and numbers assigned have some numerical meaning.

Interval = Metric = Quantitative

‘The number of people in a room’ is a Discrete interval variable because only whole numbers are possible. Height, Weight, Distance, Money, Time, Temperature, Longitude are Continuous interval variables because any fractional numbers are possible.

With Interval variables

• Order and difference are meaningful.

• If we can ask “How Much”, “How Often”, or “How many”, it is always Interval • Any variable that has only two values can be regarded as both Nominal and Interval Eg.

The...

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