Advance Statistics - Details

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- scientific discipline consisting of theory and methods for processing numerical information that one can use when, making decisions in the face of uncertainty - numerical facts (e.g. CPI, peso-dollar exchange rate)

Statistics

Two areas of statistics

Descriptive, Inferential

- methods concerned with collecting, describing, and analyzing a set of data without drawing conclusions (or inferences) about a large group

Descriptive Statistics

- used to describe a set of data in terms of its frequency of occurrence, its central tendency, and its dispersion

Descriptive Statistics

-methods concerned with the analysis of a subset of data (sample) taken from a population leading to predictions or inferences about the entire set of data.

Inferential Statistics

- it addresses the problem of making broader generalization or inferences from sample data to population

Inferential Statistics

- It is the totality of all the elements or entities from which the information are obtained

Population

- It's the finite number of objects selected from the population. It is a subset of a population

Sample

- any numerical measure or value that describes a characteristic or an aspect of a population

Parameter

- any numerical measure or value that describes a characteristic or an aspect of a sample

Statistic

- a process of collecting information from the population. It also refers to an official count by a national government of the country's population.

Census

- a process of collecting information from a sample - generally conducted when the population is too large and getting information from the whole population is costly and time-consuming task

Survey

- any characteristic or information measurable or observable in every element of the population or sample

Variable

- also known as Categorical - a variable that indicates what kind of a characteristic an individual, object, or event possesses - colors of cars, juice, fave bb team, economic status, student number

Qualitative

- a variable that indicates how much or how many of a characteristic an individual, object, or event possesses - volume, temperature, student grade, score in a quiz, height

Quantitative

- a quantitative variable that can assume only countable number of distinct values such as 0, 1, 2, 3... - number of students in a class, age as used in insurance, point-grade

Discrete

- a quantitative variable that can assume infinitely many values corresponding to the points on a line interval - weight, area, time, temperature

Continuous

- a level of measurement that is characterized by data consists of names, labels, or categories only. The data cannot be arranged in an ordering scheme - gender, civil status, blood type food preference

Nominal Level

- level of measurement involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless - nutrition status, level of consciousness, nurses' rank

Ordinal Level

- level of measurement is like the ordinal level, with the additional property that meaningful amounts of differences between data can be determined. However, there are no inherent (natural) zero starting point. - body temperature, year (1955, 1843, 1776, 1123, etc.)

Interval Level

- level of measurement is the interval modified to include the inherent zero starting point. For values at this level, differences and ratios are meaningful. - participant's age, height, weight, fluid intake, etc.

Ratio Level

- collected from the first-hand experience and is not used in the past. The data gathered are specific to the motive of the research, and highly authentic and accurate.

Primary data

- data that has been used in the past. The researcher can obtain data from the sources both internal and external to the organization

Secondary data

- refers to a sequential order of values of a variable, known as a trend, at equal time intervals. Using trends, an organization can predict the demand for its products and services for the projected time.

Time Series Analysis

- a sequential order of values of a variable

Trend

- used to eliminate a random variation from the historical demand. - helps in identifying patterns and demand levels that can be used to estimate future demand

Smoothing Techniques

- also known as the leading indicators approach used to speculate future trends based on current developments - when a past even is considered to predict the future event, the past event would act as a leading indicator.

Barometric Method

- presentation of data

Tabular, Textual, Graphical

- a single value that is used to identify the "center" of the data

Measures of Central Tendency

- most common measure of the center - also known as arithmetic average

Mean

- divides the observations into two equal parts - if number of observations is odd, the median is the middle number - if the number of observations is even, the median is the average of the 2 middle numbers

Median

- occurs most frequently - nominal average -may or may not exist

Mode

- used when sampling stability is desired - other measures are to be compared

Mean

- used when the exact midpoint of the distribution is desired - there are extreme observations

Median

- used when the "typical" value is desired - when the dataset is measured on a nominal scale

Mode

- summarizes a data set by giving a value within the range of the data values that describes its location relative to the entire data set arranged according to magnitude

Measures of Location

- raw data arranged in increasing or decreasing order of magnitude.

Array

- is the smallest value in the data set - denoted as MIN

Minimum

- is the largest value in the data set, denoted as MAX

Maximum

- Divide an array into 100 equal parts.

Percentiles

- divide an array into ten equal parts, each part having ten percent of the distribution of the data values, denoted by Dj

Deciles

- Divide an array into four equal parts, each part having 25% of the distribution of the data values, denoted by Qj

Quartiles

- a single value that is used to describe the spread of the distribution

Measure of Variation

- the difference between the maximum and minimum values in a data set

Range

- the difference between the third quartile and the first quartile

Inter-Quartile Range

- important measure of variation - shows variation about the mean

Variance

- most important measure of variation - square root of variance - has the same unit as the original data

Standard Deviation

- a measure of relative variation -usually expressed in percent - shows variation relative to mean -used to compare 2 or more groups

Coefficient of Variation

- statistical table that summarizes a set of numerical data in a comprehensive manner

Frequency Table

- is the percentage of items per category

Relative Frequency Table

- the process of estimating the value of a parameter from information obtained from a sample

Estimation

- is concerned with evaluating a claim or a conjecture about a parameter or distribution of the population

Hypothesis Testing

- a numerical value estimated for a parameter

Point Estimate

- of a parameter is an interval or a range of values used to estimate the parameter. This estimate may or may not contain the value of the parameter being estimated.

Interval Estimate

- is a specific interval estimate of a parameter determined by using data obtained from a sample ad the specific confidence level of the estimate

Confidence Interval

Of an interval estimate of a parameter is the probability that the parameter will fall within the specified interval.

Confidence Level

- measures the closeness of an estimate to its true value

Accuracy

- measures the closeness of the different possible values of the estimator to each other

Precision

- concerned with the selection of individual observations intended to yield some knowledge about a population of concern for the purposes of statistical inference.

Sampling

- means that every member of the population has a chance of being selected. If you want to produce results that are representative of the whole population, you need to use a probability sampling technique.

Probability Sampling

- Every possible sample of size n out of a population of N has an equally likely chance of occurring. - it is like pulling a number out of a hat. Every member in the population is assigned a number. However, in a large population, it can be time-consuming to write down thousands of names on slips of paper to draw from a hat.

Simple Random Sampling

- is a list of all individuals within a population. If we do not have a frame, then a different sampling method must be used.

Frame

- is obtained when we choose every k^th element in a population. -It is a method of selecting a sample from a larger population using a random starting point and a fixed, periodic interval.

Systematic Sampling

- involves selecting the sample units in groups. -It is a technique used when "natural" groupings are evident in a population. -is appropriate when it is very time-consuming or expensive to choose the individuals one at a time

Cluster Sampling

- the analysis is done on elements within each stratum - a simple random sample is drawn from each of the strata, whereas in cluster sampling only the selected clusters are studied.

Stratified Sampling

- not all members of the population has a chance of participating in the study.

Non Probability Sampling

- sampling which involves the sample being drawn from that part of the population which is close to hand - often leads to a biased study since it consists of only available people.

Convenience Sampling

- select any members of the population who are conveniently and readily available

Convenience Sample

- mainly based on ease of access. Instead of the researcher choosing participants and directly contacting them, people volunteer themselves

Voluntary Response Sampling

- This type of sampling involves the researcher using their judgement to select a sample that is most useful to the purposes of the research. - It is often used in qualitative research, where the researcher wants to gain detailed knowledge about a specific phenomenon rather than make statistical inferences.

Purposive Sampling

- choosing the participants to find more participants for making a sample group -used when participants are difficult to locate in a general population -The number of people you have accessed to "snowballs" as you get in contact with more people.

Snowball Sampling

- is the act of choosing the number of observations or replicates to include in a statistical sample.

Sample Size Determination

- an important feature of any empirical study in which the goal is to make inferences about a population from a sample.

Sample Size

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