Statistics: Sampling and Scale Observed Data

Statistics Refers to numerical facts, as an aggregate of fgures or a collection of data. Refers to a group of methods that are used to collect, analyze, present and interpret data and to arrive at conclusions or make decisions. Descriptive Statistics Deals with methods of recording/ tabulating data with their visual presentation, with the properties of various kinds of measures, with devices for computing them, and in fact, with all means of giving a summary description of the data themselves. Ex.

A supervisor in charge of 40 clerks would like to know their average salary. A sports riter wishes to list the highest goal makers in all basketball games in the last 5 NCAA seasons. Inferential Statistics Deals with inferences, conclusion, and/or forecast about an entire set of data that may be drawn from the analysis of a subset of this set of data. Ex. A tire dealer wishes to estimate the average life of a particular brand of tire. Ex. A company projects a 50% growth in the next five years after analyzing its revenue for the past five years.

Population Consist of all elements – individuals, items or objects – whose characteristics are being studied. The number of elements in a population is called population size (n). Sample It is a portion of the population selected for study. The number of elements in a sample is called sample size (n). Variable: A characteristic of the element under study which assumes different values for different elements. Qualitative Variable A variable cannot assume a numerical value and on which mathematical operations will have no meaning Ex.

Color, Civil Status, Gender Quantitative Variable A variable that can be measured numerically. Ex. Course grade, thermometer reading, monthly phone bill Discrete Variable A variable whose values are a result of counting. A quantitative variable whose set of possible values is countable. Ex. variables whose possible values are a subset of the integers, such as Social Security numbers, the number of people in a family, ages rounded to the nearest year, etc. No. of condominiums built in Manila in the last five years. No. f people who died of lung cancer in the Philippines Continous Variable A variable that can assume any numerical value over a certain interval/result of measurement. A quantitative variable is continuous if its set of possible values is uncountable. Ex. temperature, exact height, exact age Amount of soda consumed by a student in a month. Parameter Description of a characteristic of a population. Description of a characteristic of a sample. A number that can be computed from data, involving no unknown parameters. As a function of a random sample, a statistic is a random variable.

Statistics are used to estimate parameters, and to test hypotheses. Survey: Study of only a portion of the population Census Survey Study of certain characteristics of every element of a population. Sampling Survey Making inferences with a sample. Nominal Scale Observed data are merely classified into various distinct categories in which no ordering is implied. Ex. Gender, Ownership ofa house Ordinal Scale Observed data are merely classified into distinct categories w/ ranking implied in which the difference in rank is consistent in direction but not in magnitude.

Ex. Faculty rank (Lecturer / Instructor / Professor) Year level (freshmen, sophomore, Junior, senior) Interval Scale Observed data are put in an ordered scale in which the difference between the measurements in a consistent meaningful quantity. Ex. Gregorian calendar, measurement of longitude, measurement of tides Ratio Scale Observed data are put in an ordered scale in which the differences are meaningful and equal at all points on the scale and a measurement of zero means absence of he attribute being measured. Ex.

Speed or Acceleration, Salary, measure of heat in Kelvin Scale Primary Data Data observed or collected directly from first-hand experience. Secondary Data Published data and the data collected in the past or other parties Methods of Data Collection: 1. Direct – 2. Indirect – 3. Registration- It can be used to obtain complete enumeration through a legal requirement. Although registers are usually implemented for purposes other than to collect data, they can be very useful in the design and implementation of a statistical system, provided that the data they contain are reliable, timely and complete. Observation Method – In practice, observers do not only make direct measurements (observations), but also conduct interviews and surveys using questionnaires. They might also be involved in data processing and analysis. The tasks of an observer are difficult and adequate training and supervision are therefore essential. 5. Experiment Method – An experiment is a method that most clearly shows cause-and-effect because it isolates and manipulates a single variable, in order to clearly show its effect.

Experiments almost always have two distinct variables: First, an independent ariable (‘V) is manipulated by an experimenter to exist in at least two levels (usually “none” and “some”). Then the experimenter measures the second variable, the dependent variable ( V) Sampling: The process of selecting a subset of units or individuals (a portion or sample) from a population of interest so that by examining the sample, we can generalize the results to the whole population. The target population is the entire group a researcher is interested in; the group about which the researcher wishes to draw conclusions.

Advantages of Sampling: Larger sample sizes are more accurate representations of the whole The sample size hosen is a balance between obtaining a statistically valid representation, and the time, energy, money, labour, equipment and access available A sampling strategy made with the minimum of bias is the most statistically valid Most approaches assume that the parent population has a normal distribution where most items or individuals clustered close to the mean, with few extremes A 95% probability or confidence level is usually assumed, for example 95% of items or individuals will be within plus or minus two standard deviations from the mean This also means that up o five per cent may lie outside of this – sampling, no matter how good can only ever be claimed to be a very close estimate Sample Population A population is a group of phenomena that have something in common. The term often refers to a group of people. Probability Sampling: 1 . Simple-Random – Simple random sampling is the basic sampling technique where we select a group of subjects (a sample) for study from a larger group (a population).

Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. Every possible sample of a given ize has the same chance of selection; i. e. each member of the population is equally likely to be chosen at any stage in the sampling process. 2. Stratified-Random – There may often be factors which divide up the population into sub-populations (groups / strata) and we may expect the measurement of interest to vary among the different sub-populations. This has to be accounted for when we select a sample from the population in order that we obtain a sample that is representative of the population. This is achieved by stratified sampling.

A stratified sample is obtained by taking samples from each stratum or sub-group of a population. . Systemated-Random – Samples are chosen in a systematic, or regular way. a. They are evenly/regularly distributed in a spatial context, for example every two metres along a transect line b. They can be at equal/regular intervals in a temporal context, for example every half hour or at set times of the day c. They can be regularly numbered, for example every 10th house or person 4. Cluster-Random – Cluster sampling is a sampling technique where the entire population is divided into groups, or clusters, and a random sample of these clusters are selected. All observations in the selected clusters are included in the sample.