3 definitions

Population: Refers to every unit in existence

Sample: Units we have measured

Sampling (Simple Random Sampling): ensures that each member of the population has an equal chance of being picked as a part of a sample.

Descriptive Statistics: Used to describe certain aspects of a sample (eg. sample mean is 5.4 etc)

Inferential Statistics: Used to make statements about the whole population based on only what we know about the given sample.

Sampling error: Difference between statistics inferred from the sample and true population.

The larger the sample, the smaller is the sampling error. Sampling error just refers to the fact that statistics derived from a sample are only estimates of true parameters of the whole population and it has got nothing to do with error during calculation.

Sampling error of mean is the difference between sample mean and population mean.

Measurement Scales:

Nominal	Ordinal	Interval	Ratio
naming and classifying into mutually exclusive and collectively exhaustive categories	ranked according to some criteria. usually impossible to infer different members of two adjacent categories and compare it with other adjacent	order measurements based on distance between them. This is the only truly quantitative scale	Equality of ratios and equality of intervals may be determined
eg: male-female; well-sick; under 65- over 65	eg: socio-economic status - low,medium,high	eg: 10 to 20 has 10 as interval and so does 30 to 40.

naming and classifying into mutually exclusive and collectively exhaustive categories

ranked according to some criteria. usually impossible to infer different members of two adjacent categories and compare it with other adjacent

order measurements based on distance between them.

This is the only truly quantitative scale

Equality of ratios and equality of intervals may be determined

eg: male-female;

well-sick;

under 65- over 65

eg: socio-economic status - low,medium,high

eg: 10 to 20 has 10 as interval and so does 30 to 40.

Research Study: A research study is a scientific study of phenomenon of interest. Research studies involve designing sampling protocols, collecting and analyzing data, and providing valid conclusions based on results of analyses.

Experiment: Special type of research study in which observations are made after specific manipulations of conditions have been carried out; they provide the foundation for scientific research.

Ordered array: from smallest to largest values

Rule of thumb for determining class intervals: No less than 5 and no more than 15 class interval.

width of class intervals = \(w=\frac{R}{K}\) ; where \(R\) = range i.e. difference between largest and smallest number an \(k\) = number of class intervals.

k is determind by sturges’s rule

\(k=1+1.322(log_{10}n)\)

Here,

\(n\)= number of values in the data

\(k\)= number of class intervals

Note: Relative frequency ~ experimental probability ~ empirical probability