Chapter 1-Nature Of Statistics PDF

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allan hildenbrandt, stats 151, lecture notes for nature of statistics ...

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Nature Of Statistics ! Statistics is a speci!c area of study and investigation which can roughly be divided into two parts: descriptive statistics and inferential statistics.

1 De!nition Descriptive Statistics consists of methods for organizing and summarizing information. ! Techniques of descriptive statistics include graphs, charts and tables and various descriptive calculations (called numerical summaries).

2 ! In order to de!ne inferential statistics, we need to distinguish between two kinds of data collections.

De!nition : The collection of all individuals or items under consideration in a statistical study. : That part of the population from which information is actually obtained. ! The selection of a few elements from the population is called a sample. ! One of the most important problems in applied statistics is how to use the data set of a sample to determine meaningful information about the population.

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De!nition Inferential Statistics consists of methods for drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the population. ! The subject that links descriptive and inferential statistics is probability - this will be studied later in some detail.

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Observational Studies and Designed Experiments ! Once a sample has been selected from the population, the information of interest needs to be collected. ! Such a process is sometimes called a study - there are two distinct ways a study can be done.

De!nition

In an observational study, researchers simply observe characteristics and take measurements, as in a sample survey.

De!nition In a designed experiment, researchers impose treatments and controls and then observe characteristics and take measurements. ! Observation studies can reveal association, but not causation. ! Designed experiments (done properly) reveals both association and causation.

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CENSUS = EVERYONE INCLUDED

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Census, Sampling and Experimentation ! If we"re interested in a particular characteristic of a population, ideally we would collect the required information from every individual in the population. ! ! A census may appear to be an ideal way to study a population since it includes all the information., but there are problems with census taking. ! If the population is large, it can be very costly and difficult (perhaps impossible) to collect information from every member of the population. ! Since a census is usually too costly or takes too long, most statistical information is gathered by sampling or experimentation. ! ! Since the purpose of sampling is to make decisions about the corresponding population, it is important that the results obtained from sampling closely match the results that we would obtain by conducting a census. ! This means sampling must be done very carefully so as to obtain a representative sample. How can this be done? ! One method of sampling is to try to choose elements of the population so each element has an equal chance of being included in the sample.

De!nition Simple Random Sampling; Simple Random Sample Simple random sampling: A sampling procedure for which each possible sample of a given size is equally likely to the one obtained. Simple random sample: A sample obtained by simple random sampling.

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! Using an SRS (simple random sample) is a common way of obtaining a representative sample. ! Samples may be selected with or without replacement. ! In sampling with replacement, each time an element is chosen from the population, it put back in the population - thus any element may be chosen more than once for a sample. ! In sampling without replacement, an element of the population is removed from the population once it has been chosen - thus any element can only appear only once in the sample. ! In this course, we shall usually work with a SRS.

WITHOUT REPLACEMENT - putting names in a box and keeping names picked without putting it back in the box WITH REPLACEMENT - putting names drawn back into the box so that a name can be drawn more than once

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