Statistics Vocab

• The
• science that deals with the analysis and classification of empirical data.  It also attempts to draw conclusions based on
• past or present experience.

• The
• totality of all data studied.

• A
• subset of data drawn from a population.

• A numerical measurement referring to a
• population.

A numerical measurement referring to a sample.

The collection of data from every member of the population.

• It
• assumes different values. We use letters to indicate variables.

• It
• has a fixed value. It is the opposite of variable.

• A
• variable that assumes values depending on chance.

• It assumes a finite number of values, or if it
• assumes infinitely many values, the values can be counted using the counting
• numbers 1, 2, 3 … etc.

• It assumes infinitely many values that cannot be
• counted. There are no gaps between the values.

• Non-numerical data such as names, labels, categories,
• etc. They cannot be ordered.

• Like ordinal but differences make sense.  There is no natural starting point, i.e.
• there is no zero.  Ratios are
• meaningless.  For example body
• temperatures.

• They can be ordered, but differences either they
• cannot be determined or they are meaningless, i.e. rating movies using stars.

• This
• is the highest level of measurement for numerical data. There is a zero
• starting point and differences and ratios are meaningful.

• Non-numerical
• data, i.e. color, party or religious affiliation, etc.

• Categorical
• data use either the nominal or ordinal scale of measurement.

• Numerical
• data i.e. test scores, incomes figures, etc.

• Quantitative
• data use either the interval or ratio scale of measurement.

• :  A variable with
• categorical data.  

 

• Statistical analysis for categorical variables is
• limited to summarizing the data by category of computing the proportion of the
• observations in each category.

• : A variable with
• numerical data.

• The data can be manipulated mathematically and the
• results are meaningful. For example we can add the data and divide by the
• number of observations to arrive at the average value.

Data collected at one point in time.

• For example a media research company calls up 5,000
• households at random to determine the proportion of households tuned to NBC to
• watch the opening ceremony of the 2012 Olympic Games.

Data collected at regular intervals over time.

• Typical measuring points are months, for example monthly unemployment figures for the last three
• years, quarters, for example company
• quarterly reports for the last two years etc.
• The best way to represent time series data is by a
• line graph.

The variable of interest

We observe and measure specific characteristics, but we do not attempt to control or modify the subjects being studied. A Gallup poll is an example of an observational study.

all key terms

• We conduct an experiment or as we say in Statistics,
• we apply some treatment and then we observe its effects on the subjects. (The
• subjects are usually called experimental units).
• Pharmaceutical companies conduct such experiments
• when they test new drugs.

This part of Statistics attempts to summarize or describe the important characteristics of a set of data.

• Methods of summarizing data include tables, pictures such as bar charts, pies, histograms, frequency polygons,
• line-charts, etc, and numbers that
• measure a specific characteristic of the data. For example, the mean or average
• measures the center of a set of data.

• This part of Statistics attempts to make inferences or draw conclusions or generalizations
• about a large population, based on a sample drawn from that population.

• The tools used are based on Probability and Probability
• Distributions and are extremely sophisticated.

• The methods used in Statistical Inference have solid
• Mathematical foundation and they will yield valid results provided of course
• that the sample is representative of the population.

• So the weak link in Statistical Inference is the sample and the sample size. Obviously a biased sample will yield unreliable
• results.

• How to choose a “good” sample is a science in
• itself.

Each member from the population has an equal chance of being selected.

• Every
• possible sample of the same size n has an equal chance of being selected.

• Notice
• that there is difference between a random sample and a simple random sample.

• Divide
• the population into sub-populations or strata, and then draw a sample from each
• stratum.

• Note: If the sample
• selected from each stratum is a random sample, then this procedure, first
• stratification and then random sampling is called stratified random sampling. This is a subgroup of stratified
• sampling.

• Choose
• a starting point then select a specified element, say the kth
• element.

• Divide
• the population into sections or clusters, choose a few clusters at random, and
• then perform a census within each
• selected cluster. This means select all
• the elements from the chosen clusters.

• A
• special case of cluster sampling is area
• sampling, where the clusters are geographic subdivisions.

• Just
• choose data readily and conveniently available. This does not yield
• statistically valid results.

• A voluntary response sampling is one in which the
• respondents themselves decide whether to be included or not.

• Such
• a sample is flawed and should not be used for making general statements about a
• population.

Sampling schemes that combine several sampling methods are called multistagesamples.