Mathematics in The Modern World - Data Management

Data

are raw information or facts that become useful information when organized in a meaningful way. It could be of qualitative and quantitative nature.

Data Management

is concerned with 'looking after' and processing data.

Importance of Data Management

Ensures that data for analysis are of high quality so that conclusions are correct; allows further use of the data in the future and enables efficient integration of results with other studies; leads to improved processing efficiency, improved data quality, and improved meaningfulness of the data.

Census

this is the procedure of systematically acquiring and recording information about all members of a given population.

Sample Survey

sampling is a selection of a subset within a population, to yield some knowledge about the population of concern.

Experiment

this is performed when there are some controlled variables (like certain treatment in medicine) and the intention is to study their effect on other observed variables (like health of patients).

Observation study

this is appropriate when there are no controlled variables and replication is impossible. This type of study typically uses a survey.

Characteristics of a well-designed and well-conducted survey

A good survey must be representative of the population; incorporates a chance, such as a random number generator; the wording of the question must be neutral; possible sources of errors and biases should be controlled.

Nonprobability sampling

is any sampling method where some elements of the population have no chance of selection or where the probability of selection can't be accurately determined.

Probability Sampling

it is possible to both determine which sampling units belong to which sample and the probability that each sample will be selected.

Simple Random Sampling (SRS)

all samples of a given size have an equal probability of being selected and selections are independent.

Systematic Sampling

relies on dividing the target population into strata (subpopulations) of equal size and then selecting randomly one element from the first stratum and corresponding elements from all other strata.

Stratified Sampling

when the population embraces a number of distinct categories, the frame can be organized by these categories into separate 'strata'.

Cluster Sampling

sometimes it is cheaper to 'cluster' the sample in some way (e.g. by selecting respondents from certain areas only, or certain time-periods only).

Matched random sampling

in this method, there are two (2) samples in which the members are clearly paired, or are matched explicitly by the researcher.

Characteristics of a well-designed experiment

Stating the purpose of research, including estimates regarding the size of treatment effects, alternative hypotheses, and the estimated experimental variability.

Design of experiments

using blocking (to reduce the influence of confounding variables) and randomized assignment of treatments to subjects.

Examining the data set

in secondary analyses, to suggest new hypotheses for future study.

Documenting results

presenting the results of the study.

Control groups

To be able to compare effects and make inference about associations or predictions, one typically has to subject different groups to different conditions.

Random Assignments

the second fundamental design principle is randomization of allocation of (controlled variables) treatments to units.

Replication

All measurements, observations or data collected are subject to variation, as there are no completely deterministic processes.

Confounding

a confounding variable is an extraneous variable in a statistical model that correlates (positively or negatively) with both the dependent variable and the independent variable.

Placebo

a placebo is an imitation pill identical to the actual treatment pill, but without the treatment ingredients.

Blinding

a method used to prevent bias in research by keeping participants unaware of which treatment they are receiving.

Blocking

is the arranging of experimental units in groups (blocks) that are similar to one another.

Completely randomized designs

are for studying the effects of one primary factor without the need to take other nuisance variables into account.

Randomized block design

is a collection of completely randomized experiments, each run within one of the blocks of the total experiment.

Chi-square test

is used to determine whether there is significant difference between the expected value frequencies and the observed frequencies in one or more categories.

Chi-square goodness of fit test

determines if a sample data matches a population.

Chi-square test for independence

compares two (2) variables in a contingency table to see if they are related.