STAT111: PRELIM (TERMINOLOGY & DEFENITION)

Statistics

Is a systematic and scientific process of collection, presentation, analysis and interpretation of gathered data

1. Descriptive Statistics

2. Inferential Statistics

Branches of Statistics

Descriptive Statistics

Description, collection, and presentation

Inferential Statistics

Conclusion, analysis, and interpretation

1. Qualitative Data

2. Quantitative Data

Branches of Data

1. Discrete

2. Continous

Types of Quantitative Data

1. Primary

2. Secondary

Types of Data

Variable

A variable is any property or characteristic of some event, object, or person that may have different values at different times depending on the conditions

Constant

is the opposite of variable, because the value are never changing

1. Independent Variable

2. dependent Variable

Types of Variable

1. Nominal

2. Ordinal

3. Interval

4. Ratio

Levels of Measurement

Nominal

Data are used to identify, classify or categorize

Nominal

It is can be qualitative or quantitative information

Nominal

For quantitative, this number losses its numerical value

Ordinal

Data that shows ranking, order or sequence

Ordinal

It can be also used to categorize or classify

Ratio and Interval

Data that can serve the purpose of nominal and ordinal

Ratio and Interval

Both of these can measure the degree of difference between subjects

Interval

Doesn't have an absolute zero value

Ratio

Has the absolute zero value

1. Interview Method

2. Questionnaire Method

3. Registration Method

4. Observation Method

5. Experimentation Method

Types of Data Collection

1. Textual

2. Tabular

3. Graphical

Types of Data Presentation

1. Pie Chart

2. Bar Graph

3. Pictograph

The appropriate graphical representation for your data: Categorical Data

1. Histogram

2. Scattered Plot

3. Frequency Polygon

4. Ogive Curve

5. Line Graph

The appropriate graphical representation for your data: Numerical Data (Ratio & Interval)

Population

It is defined as the totality of the subject that wish to study or analyze

Sample

It is a small group taken from a population

Parameters

Is the characteristics of the population

Statistic

Is the characteristics of the sample

Power Analysis

Is the calculation used to estimate the smallest sample size needed for an experiment, given a required significance level, statistical power, and effect size

Sampling

It is the process of selecting the sample members from your population

1. Probability Sampling

2. Non-Probability Sampling

Sampling Techniques

Probability Sampling

Is a set of sampling methods where in each member of the population is given the chance in the selection process. It requires randomness

Non-Probability Sampling

Is a set of sampling methods where in only the special members of the population will be part in the selection process. It does not require randomness

1. Pure Random Sampling

2. Systematic Sampling

3. Stratified Sampling

4. Cluster Sampling

Types of Probability Sampling

1. Quota Sampling

2. Convenience sampling

3. Purposive Sampling

4. Snow Ball Sampling

Types of Non-Probability Sampling

Pure Random Sampling

Is a method where in the sample members are select by picking randomly from the population

Pure Random Sampling

It is also called SRS or simple random sampling

Pure Random Sampling

It is also called as lottery sampling

Systematic Sampling

It's a process of sampling that select a desired element (kth element) from the population until the entire sample size is obtained

Stratified Sampling

It's a process of sampling where in the population is divided unto subgroups (strata) then drawing individual from each subgroup (stratum) to complete the sample group

Cluster Sampling

Also called area sampling

Cluster Sampling

It is the sampling where in group is chosen as the sample members

Convenience Sampling

Choosing a sample who are available during the time of sampling. Also called Accidental Sampling

Quota Sampling

Choosing a sample based on the assigned quota of the researcher and taking into the consideration of his discretion or choice

Purposive Sampling

A sampling technique that choose sample that are in-lined to the purpose of the researcher

Snow Ball Sampling

Is a sampling technique that chose sample based on the referral of the other sample member

Frequency Distribution (Qualitative Data)

Establish the category in a given set of information

Frequency Distribution (Qualitative Data)

Tally the data against the created category

Frequency Distribution (Qualitative Data)

Express the tally in frequency

Frequency Distribution (Qualitative Data)

Compute the Relative Frequency and the Percentage

Range

Is the distance between the highest and the lowest values

Interval

Is the number of values in each class

1. Frequency Polygon

2. Histogram

3. Ogive Curve

Frequency Distribution (Quantitative Data)

Mean

Tells you the quality of the magnitudes of the data

Median

Tells you the middle position data

Mode

Tells you the most common items in the data

1. Unimodal

2. Bimodal

3. Trimodal

4. Multimodal

Types of Mode

Weighted Mean

Is the averaging of values which have are not equally represented

Quantiles

Is a measurement of position

Quantiles

It is the process of dividing a set of data into several equal parts

1. Quartile

2. Decile

3. Percentile

Measures of Position

Quartile

Divides the data into 4 equal parts (Q1, Q2 and Q3)

Decile

Divides the data into 10 equal parts (D1, D2, D3,... and D9 )

Percentile

Divides the data into 100 equal parts

Percentile Rank

It tells you what percent of the cases got below the rank position. Denoted by PR

Percentile Point

Is the score or value that corresponds to the given percentile rank. Denoted by Pn

Measures of Variability or Dispersion

Measurement of degree of scatteredness in a set of data

1. Range

2. Standard Deviation

3. Variance

4. Mean Absolute Deviation

5. Quartile Deviation

6. Decile Deviation

7. Percentile Deviation

Measure of Dispersion

Range

Is the distance between the HIGHEST AND LOWEST DATA (R)

Standard deviation

Is the squared average distance of each item from the mean (s or 𝜎)

Variance

Is the square value of the standard deviation (𝑠^2 or 𝜎^2)

Mean Absolute Deviation

Is the absolute distance of each data from the mean(MAD)

Quartile Deviation

Is the half distance between the Q1 and Q3 (QD)

Percentile Deviation

Is the distance between the P10 and P90 (PD)

Decile Deviation

Is the distance between D1 and D9 (DD)

Coefficient of Variation

Is used to compare the variation of several sets of data without having the same unit of measures. Devoted by CV

Skewness

Is a measurement of departure from the symmetry of a distribution

Normal Distribution

Means a balance and well distributed set of data

Skewed Distribution

Means unbalanced distribution of set data

Positively Skewed

It is composed of two of more higher values data

Negatively Skewed

It is composed of more lower values data

Skewness Coefficient

Is a number that represent the degree of skewness. It is denoted by SK

Kurtosis

Is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution

1. Mesokurtic Distribution

2. Leptokurtic Distribution

3. Platykurtic Distribution

Type of Distribution based on Kurtosis

Mesokurtic Distribution

Shows an excess kurtosis of zero or close to zero. This means that if the data follows a normal distribution, it follows a mesokurtic distribution

Leptokurtic Distribution

Indicates a positive excess kurtosis

Leptokurtic Distribution

Shows heavy tails on either side, indicating large outliers. In finance, it shows that the investment returns may be prone to extreme values on either side. Therefore, an investment whose return follows this distribution is considered to be risky

Platykurtic Distribution

Shows a negative excess kurtosis; The kurtosis reveals a distribution with flat tails

Platykurtic Distribution

In the finance context, this type of distribution of the investment returns is desirable for investors because there is a small probability that the investment would experience extreme returns