Stats

Statistics is defined as the art and science of collecting analyzing, presenting, and interpreting data.

Data is the facts and figures collected, analyzed, and summarized for presentation and interpretation.

Data Set is all the data collected in a particular study.

Elements are the entities on which data are collected. eg. the individual players in the NHL being studied. ((left side of Data Set/ascending order)

Variable is a characteristic of interest for the elements. eg continuing with the NHL players as elements the variables could be goals scored, assists per game and number of years played in NHL

Observation is measurements collected on each variable for every element in a study provide the data.  The set of measurements obtained for a particular element is the observation (conclusion for element).

Scale of Measurement determines the amount of information contained in the data and indicates the most appropriate data summarization and statistical analyses.

Nominal Scale is when the data for a variable consist of labels or names used to identify an attribute of the element, the scale of measurement is considered a nominal scale.

Ordinal Scale is the data exhibits the properties of nominal data and the order or rank of the data is meaningful. (when data is ranked or ordered) eg. when a business is collecting data and gives predefined responses in ranking form 1.excellent service 2. good service 3. satisfactory service 4. poor service

Interval Scale is the data have all the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure. Interval scale is always numerical. eg. student SAT math scores 620,550,470 can be ranked or ordered in terms of best performance to poorest performance in math.

Ratio Scale is data has all the properties of interval data and the ratio of two values is meaningful.  Variables such as distance, height, weight, and time use the ratio scale of measurement.  **This scale requires that a zero value be included to indicate that nothing exists for the variable at the zero point. eg. A zero value for the cost a automobile would indicate the vehicle has no cost and is free.  If one where to compare the cost of 30000 for one vehicle to the cost of 15000 for the second vehicle, the ratio property shows that the first automobile is 30000/15000=2 times the cost of the second vehicle.

Categorical Data is data that can be grouped by specific categories. Categorical date uses either the nominal or ordinal scale of measurement.

Quantitative Data is data that uses numerical values to indicate how much or how many. Quantitative data are obtained using either the interval or ratio scale of measurement.

Categorical Variable is a variable with categorical data. If a variable is categorical, the statistical analysis is limited.  We can summarize categorical data by counting the number of observations in each category or by computing the proportion of the observations in each category

Quantitative Variable is a variable with quantitative data.  Arithmetic operations provide meaningful results for quantitative variables. eg. quantitative data may be added and then divided by the number of observations to compute the average value.

Cross-sectional data are data collected at the same or approximately the same point in time.  eg. the data collect on individual players in the NHL for a certain year.

Time series data are data collected over several time periods. eg. the time series in NHL player stats from 2006-2009.

Experimental study is when a variable of interest is identified.  Then one or more other variables are identified and controlled so that data can be obtained about how the influence the variable of interest.  e.g. a pharmaceutical firm might be interested in conducting an experiment to learn about how a new drug affects blood pressures.  blood pressure is the variable of interest in the study.  The dosage level of the new drug is another variable that is hoped to have a causal effect on blood pressure.  To obtain data about the effect of the new drug, researchers select a sample of individuals. The dosage level of the new drug is controlled, as different groups of individuals are given different dosage levels.  Before and after data on blood pressure are collected for each group.

Observational study makes no attempt to control the variables of interest.  A survey is perhaps the most common type of observational study. e.g. a restaurants survey- to obtain a customers opinions on the quality of food, quality of service, atmosphere, and so on.

Data Acquisition is an errors in the data value obtained is not equal to the true or actual value that would be obtained with a correct procedure. e.g. writing the age of person as 42 when it should be 24. Another example is when a person answering an interview question might misinterpret the question and provide and incorrect response.

Descriptive Statistics consists of data that are summarized and presented in a form that is easy for the reader to understand. e.g.  summaries of data, which may be tabular, graphical, or numerical are easy to interpret and digest.

Population is the set of all elements of interest in a particular study. e.g. the Canadian population in 2014.

Sample is a subset of the population

Census is the process of conducting a survey to collect data from the entire population.

Sample Survey is the process of conducting a survey to collect data for a sample.

Statistical Inference the use data from a sample to make estimates and test hypotheses about the characteristics of a population.

Sampled population is the population from which the sample is drawn from. e.g. is all registered voters of a province.

Frame is a list of the elements that the sample will be selected from.  e.g. continuing with the voters scenario, the Frame is the list of all the registered voters.

Parameters is the numerical characteristics of a population.

A Simple Random Sample of size n(n=sample size) from a finite population of size N(N=population)is a sample selected such that each possible sample of size n has the same probability of being selected.

Sampling without replacement is when any previously used random selection is ignored because the corresponding selection is already included in the sample

Sampling with replacement is when previously used random selections are acceptable and specific selections could be included in the sample two or more times.

• Random Sample is of a size n from an infinite population is a sample selected such that the following conditions are satisfied:
• 1. Each element selected comes from the same population
• 2. Each element is selected independently

Stratified Random Sampling is the elements in the population are first divided into groups called strata, such that each element in the population belongs to one and only one stratum.  The basis for forming the strata, such as department, location, age, industry type, and so on, is at the discretion of the designer of the sample. The best results are obtained when the elements within each stratum are as much alike as possible.  If strata are homogeneous, the stratified random sampling procedure provides results just as precise as those of SRS.

Cluster Sampling is the elements in the population are first divided into separate group called clusters.  Each element of the population belongs to one and only one cluster.  A Simple random sample of the cluster is then taken.  All elements within each sampled cluster form the sample. Cluster sampling tends to provide the best results with the elements with the clusters are not alike. In the ideal case, each cluster is a representative small-scale version of the entire population. The value of cluster sampling depends on how representative each cluster is of the entire population. e.g. when conducting area sampling and the use of city blocks or other well defined areas can be used as clusters.

Systematic Sampling is if a sample size of 50 is desired from a population containing 5000 elements, we will sample one element for every 5000/50=100 elements in the population. A systematic sample for this case involves selecting randomly one of the first 100 elements from the population list. Other sample elements are identified by starting with the first sampled element and then selecting every 100th element that follows in the population list.

• Convenience Sampling is a nonprobability sampling technique.  As the name implies the sample is identified primarily by convenience.
• e.g. a professor conducting research at a university may use student volunteers to constitute a sample simply because they are readily available and will participate as subjects for little or no cost.

Judgment Sampling is a nonprobability sampling technique where the person with most knowledge on the subject of the study selects elements of the population that he or she feels are most representative of the population.  e.g. when a reporter samples two or three senators, judging that those senators reflect the general opinion of all senators.