Data Analytics Exam 1

Population

The set of all items of interest in a statistical problem

Ex: Houses in Roanoke

Parameter

A descriptive measure of a population

Ex: Mean (average) appraised value of all houses

Sample

A set of items drawn from a population

Ex: 100 randomly selected houses

Statistic

A descriptive measure of a sample

Ex: Mean appraised value of selected homes

Statistical Inference

The process of making an estimate, prediction, or decision based upon sample data

Qualitative

Categorical

Ex: Brand names

Quantitative

Numbers

Ex: Number of bedrooms

Cross-Sectional

Observations in a sample that are collected at the same time

Time Series

Data that is collected at different points in time

N

Size of population

n

Size of sample

μ

Population mean

x̄

Sample mean

σ²

Population variance

σ

Population standard deviation

s²

Sample variance

s

Sample standard deviation

Measures of Central Tendency

Mean, Median, Mode

Mean

Average

Median

The middle number

Percentiles

By 1’s??

Ex: Score in the 95th percentile? Your score is ≥ 95% of other scores in the group. This does not mean you made a 95%

Mode

Most frequently occurring number

CAN BE BIMODAL OR MULTIMODAL, DO NOT BE FOOLED

Measures of Dispersion

Range, Standard Deviation, and Variance

Dispersion is also known as

The spread or range of variability

Range

High minus low

A normal bell curve means

Mean = Median = Mode, tails are asymptotic, kurtosis is 0

Asymptotic

Close to the horizontal axis (x-axis) but never reach it

Standard Deviation

The standardized measure of distance from the mean, the positive square root of the variance

What percent of cases fall within one standard deviation from the mean?

68%

What percent of cases fall within two standard deviations from the mean?

97%

Shape of Data

Skewness and Kurtosis

Skewness

Measures the asymmetry of data

Positive Skew

Right skewed/longer right tail

Negative Skew

Left skewed/longer left tail

Kurtosis

Measures the peakedness of the distribution of data

High Kurtosis

Leptokurtic

Data has more outliers

Low Kurtosis

Platykurtic

Data has fewer outliers, values are more spread out evenly

Normal Kurtosis

Mesokurtic, data has normal distribution with a moderate number of outliers

What is the goal of graphing?

1. Presentation of descriptive statistics

2. Presentation of evidence

3. Some people understand better with visual aids

4. Provides a sense of the underlying data generating process (scatter-plots)

Statistical Studies

Observational, experimental

Observational

No attempt is made to control or influence the variables of interest

Experimental

Conducted under controlled conditions, provides more information compared to data obtained from existing sources/observational studies

Considerations on Data Acquisition

1. Time requirement

2. Cost of acquisition

3. Data errors

Analytics

The scientific process of transforming data into insight for making better decisions

Descriptive Analytics

What has happened in the past

Predictive Analytics

Models constructed from past data to predict the future or to asses the impact of one variable on another

Prescriptive Analytics

Yield the best course of action

The three V’s

Volume, Velocity, Variety

Volume

The amount of available data

Velocity

The speed at which data is collected and processed

Variety

Different data types

Unethical Behavior in Statistical Study

1. Improper sampling

2. Inappropriate analysis of the data

3. Development of misleading graphs

4. Use of inappropriate summary statistics

5. Biased interpretation of the statistical results

Quartile

Q1 = 25th percentile

Q2 = 50th percentile

Q3 = 75th percentile

Interquartile Range

Q3-Q1

Variance

Based on the difference between the value of each observation and the mean

Coefficient of Variation

Usually expressed as a percentage, measures how large the standard deviation is relative to the mean, (Standard deviation / mean) * 100%

Covariance

Measures how two variables change together in a linear way (there will be a direction indicating the relationship)

Correlation Coefficient

A measure of the relationship between x and y that is not affected by the units of measurement, CORRELATION IS NOT CAUSATION

The hypothesis test will be two tailed if

Null and alt are equal and inequal

The hypothesis test will be one tailed if

The null and alt are >< or equal to

Type I Error

Rejecting null when it is true, false positive

Level of significance

The probability of making a Type I Error

Type II Error

Accepting null when it is false, false negative

p-value

The probability of observing results as extreme as the sample, assuming null is true

p is less than or equal to a

Reject null

p is greater than a

Fail to reject null

Confidence Interval

A range of values that is used to estimate an unknown population parameter

t-test

Compares means of two sets of data and notes if there is an observable difference between the two

t is

an observed difference / standard error

p = 0.05

5% chance of making a Type I Error, 95% confidence

p = 0.01

1% chance of making a Type I Error, 99% confidence

The type of tail is determined by

Alternative hypothesis

t equation

t equals x bar minus mu divided by standard deviation divided by the square root of the sample number (n)

Degrees of Freedom (df)

Measures how much independent information is available to estimate variability

df is generally

n - 1

Random/Simple Random Sampling

Equal chances for all, unbiased, most widely used

Stratified Sampling

Ensures all groups are represented

Quota

Quick, non-random, guarantees proportions, based on convenience and faster/cheaper, non-probability

Purposive

Participants with specific traits or expertise, informative but subjective (non-probability)

Cluster

Efficient for large, spread out populations

Systematic

Regular interval selection, simple to apply, selecting every kth individual

Sampling

The process of selecting a subset of indivs or items from a pop to estimate characteristics of the whole, studying the entire population is usually impractical and costly