stats

sampling

selection of subset or statistical sample

Population

all members that meet a set of specifications.

element

a single member of any given population

sample

some elements that are selected from population

census

all elements are included

Probability and Non-Probability sampling

Two major sampling techniques

Probability

• respondents are randomly selected to take part in a survey or other mode of research.

• each person in a population must have an equal chance of being selected.

Non-Probability Sampling

sample is created through a non-random process. This type of sampling would also include any targeted research that intentionally samples from specific lists. It can be a more cost-effective and faster approach than probability sampling and can also introduce bias into the sample and results.

• Convenience Sample

• Snowball sample

• Quota Sample

• Purposive or Judgemental sample

Different Non-Probability Sampling

• simple random sample

• stratifiee random sample

• cluster sample

• systematic sample

Different Probability Samplings

Convenience Sample

this method uses people who are convenient to access to complete a study.

Snowball sampling

works by recruiting some sample members who in turn recruit people they know to join a sample. This method works well for reaching very specific populations who are likely to know others who meet the selection criteria.

Quota sample

a population is divided into subgroups by characteristics (such as age or location) and targets are set for the number of respondents needed from each subgroup.

Purposive or Judgemental sample

the sample selection is left up to the researcher and their knowledge of who will fit the study criteria.

Sampling Bias

Non-Probability sampling is also known as

Simple Random Sample

each member of a population is assigned an identifier such as a number, and those selected to be within the sample are picked at random, often using an automated software program.

Stratified Random Sample

the population is divided into sub-groups, (such as male and female) and within those sub-groups a simple random sample is performed. This enables a random sample that is representative of a larger population and its specific makeup, such as a country's population.

cluster sample

a population is divided into clusters which

are unique, yet represent a diverse group - for example, cities are often used as clusters. From the list of clusters, a select number are randomly selected to take part in a study.

Systematic Sample

participants are selected to be part of a sample using a fixed interval. For example, if using an interval of 5, the sample may consist of the fifth, 10th, 15th, and 20th, and so forth person on a list.

sampling variation

refers to the natural differences that occur when we take multiple samples from the same population.

• Tangible Population

• Conceptual Population

Types of Population

Tanginble Population

populations consisted of actual physical objects such as the students, concrete blocks, bolts. This are always finite and after an item sampled, the population size decreases by 1.

Conceptual Population

A simple random sample may consist of values obtained from a process under identical conditions. This sample comes from a population that consists of all the values that might possibly have been observed.

Using scatter plotting. The data used simple random sampling when the data or values do not show a pattern or trend

How do we consider that the datas are collected using simple random sampling?

Independent

values of some data/item does not help to predict the values of the others.

Sampling with replacement

method of sampling where each item ia returned to a set after being selected.

Independent sampling

means that each sample is selected in such a way that it does not influence the selection of other samples.

One-sample experiment

only one population of interest and a single sample is drawn from it.

Multisample experiment

2 or more populations of interest and a sample is drawn from. each population.

Factorial experiments

In many multisample experiments, the populations are distinguished fron one another by the varying of one or more factors that may affect the outcome

• controlled experiment

• Observational experiment

Example of 2×2 Factor Experiment

Controlled experiment

is a scientific test done under controlled conditions, meaning that just one (or a few) factors are changed at a time, while all others are kept constant.

Observational Study

are individuals are observed or certain outcomes are measured. No attempt is made to affect the outcome (for example, treatment is given).

sample mean

also called the "arithmetic mean," or, more simply, the "average." It is the sum of the numbers in the sample, divided by how many there are.

Sample mean = Sum of X/n

sample mean formula

standard deviation

quantity that measures the degree of spread in a sample

mew²= sum of (x-u) ²/N

population variance

s² = sum of (x - sample mean) ²/ n-1

sample variance

s = √(sum of (x-sample mean)²/n-1

sample standard deviation

outliers

sample containing a few points that are much karger or smaller than the rest.

Median

like the mean, is a measure of center or the middle value in a set of data.

median = (n+1/2) th

is n is odd, formula of median is

median =[(n/2) th + )(n/2+1) th/2]

if n is even, the formula of median is

trimmed mean

A measure of center that is designed to be unaffected by outliers.

is computed by arranging the sample values in order, "trimming" an equal number of them from each end, and computing the mean of those remaining.

mode

most common number that appears in your set data

range

difference between highest and lowest values

Quantiles

are values that split sorted data in equal parts.

Quartiles (4-quantiles):

Three quartiles split the data into four parts.

Deciles (10-quantiles)

Nine deciles split the data into 10 parts.

Percentiles (100-quantiles):

99 percentiles split the data into 100 parts.