Statistics and Probability

Statistics - is the SCIENCE of Planning studies, collecting, organizing, presenting, analyzing or summmarizing, interpreting, and drawing conclusion based on the data. It is also a way of reasoning, along with a colection of tools and methods designed to help us understand the world.

==Collection== - process of obtaining information.

==Organization== - determining/ascertaining manner of of presenting the data into tables/graphs or chart so that logical and statistical conclusion can be drawn from collected measurement.

==Analysis of data== - process of ==extracting from the given data relevant information== from which numerical description can be formed.

==Interpretation of Data== - task of ==drawing conclusions== from the analyzed data.

Probability - is the chance that something will happen

Descriptive - collection, organization, presentation, analysis/summarization of data.

Inferential - using a sample to interpret and draw conclusion based on the data or about a population

Inferential - Percentages and sample size

Descriptive - data as a whole

Universe - collection or set of entities from whom we got the data

Population - the set of all possible values of a variable

Parameter - It is a value that tells or describe something about a population

Sample - subgroup of a population

Statistic - value that tells or describe something about a sample

Variable - a characteristic that is observable and measurable in every unit of a universe

Qualitative - non-numeric and express categorical attributes

Quantitative - numerical data

Types of quantitative data

1. Discrete data - data that can be counted
2. Continuous data - data that can be measured

Central Tendency of Ungrouped Data

Mean - Average, add all value then divide by how many the number is ( arranged in lowest to highest)

Median - middle value, arrange chronologically

Mode - most appearing number

One mode - unimodal

Two modes - bimodal

3 or more modes - multi modal

None - non-modal

LEVEL OF MEASUREMENT

Nominal level - simplest form of measurement. Used to classify for purely ==classification and identification==

Ordinal - variable are ==rank ordered== according to their magnitude or intensity

Interval Level - ==no true zero point==, expressed in real number so that data can be ranked.

Ratio level - represent the most ==precise level of measurement==

PROBABILITY DISTRIBUTION

Concept of random variable

statistical experiment - used to describe any process by which ==several chance observations are obtained==.

sample space - all ==possible outcomes== of an experiment

Random variable - variable whose value is ==determined by the outcome of a random experiment== or an event.

Discrete Random Variable - set of ==assumed values is uncountable== (arises from measurement)

Discrete probability distribution - is a table listing all possible values that a discrete variable can take on, together with the associated probabilities.

NORMAL DISTRIBUTION

Normal Probability distribution - is a data distribution where the mean, median, and mode are equal and the distribution is clustered at the center

Graph of normal distribution - symmetrical bell-shaped curve along the mean and extends indefinitely in both directions

Total area under the normal curve - is equal to 100%or 1, or 50% or 0.5 to each side from the center.

STANDARD SCORE or Z-SCORE - equivalent value of a raw score expressed in terms of the mean and standard deviation of the distribution.

Different types of curves according to skewness

Negatively skewed - skewed to the left and the mean has the lowest value among the three measures of central tendency.

Positively skewed - skewed to the right and the mean has the highest value among the three measures of central tendency.

No skew - all measures of central tendency are equal

Different types of curves according to kurtosis

Mesokurtic - Normal distribution, Kurtosis = 0

Leptokurtic - High degree of peakedness, Kurtosis > 0

Platykurtic - Low degree of peakedness, kurtosis < 0

THE AREA OF A NORMAL CURVE

Z-table - area under the normal curve

Case 1 - only one side of the curve is WHOLY shaded, either left or right

Case 2 - two sides of the curve are shaded, both negative and positive ( Addition)

Case 3 - one side of the curve is shaded but only limited (Subtraction)

Case 4 - one side of the curve is halfly shaded up to the end of the tail with subtracting the area of the normal curve 0.5000

Case 5- both sides of the curve is shaded up to the end of the tail with adding the area of the normal curve 0.5000

SAMPLING DESIGN

Basic concepts and procedures

Frame – ==a collection of units, (referred to as sampling units) in a population==;
the materials or devices, which delimit, identify and allow access to the
elements of the target population.

Survey – This refers to a ==method of collecting information== about a
population in which direct contact is made with the units of study through
systematic means such as ==questionnaires and interview schedules==.

o Census or complete enumeration - This is a survey in which data are to be collected from all elements of the target population.

o Sample survey - This refers to the gathering of information from only a fraction of the population chosen to represent the whole.

Sampling – a ==process of selecting samples== from a given population.

SAMPLING TECHNIQUE

Sampling technique can be grouped into how selections of items are made
such as probability sampling and nonprobability sampling.

Probability Sampling – the ==sample is a proportion of the population== and such
sample is selected from the population by means of systematic way in which
==every element of the population has chance of being included== in the sample.

Non-Probability Sampling – The sample is not a proportion of the population and there is ==no system in selecting the sample==. The ==selection depends on the situation.==

TYPES OF PROBABILITY SAMPLING

Pure Random Sampling – Is one in which ==everyone== in the
population of the study ==has an equal chance of being selected== to be
==included== in the sample.

Systematic Random Sample –In this method, a ==research
develops an accurate sampling frame==, selects elements from
sampling frame according to ==mathematically random
procedure==, and then ==locates the exact element== that was
selected for ==inclusion== in the sample.

Stratified Random Sampling – It involves ==splitting subjects
into mutually exclusive groups== and then using ==simple random
sampling to choose members== from groups.

Cluster Random Sampling – It is a way to ==randomly select participants
from a list that is too large for simple random sampling.== For example, if
you wanted to choose 1000 participants from the entire population of the
Philippines, it is likely impossible to get a complete list of everyone.
Instead, the researcher randomly selects areas (i.e. cities or province)
and ==randomly selects from== within those ==boundaries==.

Multi - stage Sampling - Selection of the ==sample is done in two or more
steps or stages, with sampling units varying in each stage==. The
population is first divided into a number of first-stage sampling units from
which a sample is drawn. Smaller units, called the secondary sampling
units, comprising the selected first stage units then serve as the
sampling units for the next stage. If needed additional stages may be
added until the units of observation for the survey are clearly identified.
The smaller units comprising the samples selected from the previous
stage constitute the frame for the stages.

TYPES OF NON-PROBABILITY SAMPLING

Accidental Sampling – There is ==no system of selection== but only those whom the
researcher or interviewer ==meets by chance==.

Quota Sampling – There is ==specified number of persons of certain types== is
included in the sample.

Convenience Sampling – is a process of ==picking out people in the most
convenient and fastest way== to get reactions immediately. This method can be
done by ==telephone interview to get the immediate reactions== of a certain group of sample for a certain issue.

Purposive Sampling – It is ==based on certain criteria laid down by the
researcher==. ==People who satisfy the criteria are interviewed==. It is used to
determine the ==target population== of those who will be taken for the study.

Snowball Sampling – It is where ==research participants recruit other
participants== for a test or study. It is ==used when potential participants are
hard to find.==