Data Analytics - Background overview

Introduction to Data Analytics

What is data?

• Information collected regarding a subject

• expressed through rows and columns

What do rows represent in data?

Cases or observations

What do columns represent in data?

Variables

Variables

• Anything that can be changed 

• You ask every single observation (data point) for the answer to that question

Types of Variables

• Categorical (qualitative)

• Quantitative

Quantitative data

Numerical values 

• Only price and quantity are quantitative.

• Needs to use numbers to measure something getting bigger. 

“How many” or “how much.

Qualitative data (Categorical)

Descriptive and subjective

• Answers questions such as “why” or “how?"

• Includes

  • Names categories

Identifiers

• A categorical variable  

• Does not have units  

• Helps to combine different datasets and makes relational databases possible

• Are not to be analyzed! 

Time series

• Data that is gathered at regular intervals over time.

  • Temperature of days in September

Cross-sectional data

• When data for several variables are measured at the same point in time

  • Determining sales revenue, number of customers, and expenses for the last month of business.

Primary Data

collected by the researcher/analyst.

• Very expensive to collect 

  • However, this is good but can be tailored to your specific research question. 

Secondary Data

Collected by another party, like Statistics Canada obtained by the researcher/analyst.  

Population

• The group you are interested in  

  • Doesn't have to be everyone, but is still a big portion. 

• The population is more important than the sample. 

Sampling

• The population is too big and costly

• Insight into the behaviours of a population

Features of Sampling

1. Examine a part of the whole (Questions designed to give us

   answers on some characteristics of the sample)

2. Randomize (gives a better, representative sample)

3. Sample size matters (determines what we can conclude).

   from the data regardless of the size of the population)

Sample statistics

Relative to the population parameter 

Population parameter

Key numbers (that represent reality) used in a model for a population

For example: How much a McMaster student spends on food every day 

Simple Random Sample (SRS)

A sample where every possible group of the chosen size has an equal chance of being selected.

Sampling Frame

• A complete list of individuals or cases from which the sample is drawn.

• Each individual is assigned a number, and random numbers are used to select the sample.

Other Random Sample Designs

• Stratified sampling

• Cluster sampling

Stratified sampling

• Divide into similar groups (strata)

• Randomly sample within each group

• Main benefit: Reduces variability.

Clustered sampling

• Divide into representative clusters. Randomly select clusters and survey all members.

• Unbiased if clusters reflect the population.

Bar Chart

• Displays the distribution of one categorical variable, showing the counts for each category

• Next to each other for easy comparison

Pie Charts

• Show the whole group as a circle (“pie””) sliced into pieces.

• The size of each piece is proportional to the fraction of the whole in each category.

Frequency Tables

• Organizes data by recording counts and category names as in the table below.

Example below

• Frequency table of the number of Loblaw stores in eastern Canada

Relative frequency table

• Displays the proportions or percentages that lie in each category rather than the counts

Example below:

• Showing percentages of Loblaw stores in eastern Canada

Contingency Table

• Shows how one variable depends on or is related to another variable.

  • We may display the data as a percentage – as a row

    percent, column percent, or a total percent

Conditional Distributions

• Distribution of a variable restricted to a specified group.

• Example below:

  • To show how social network use is varied by countries, we can display the data in a contingency table

Very important to understand what these types of questions are asking 

 

For example, the number of people from surveys who responded with YES and were from Germany: 340 / 5039 

 

What proportion of those who are from Germany (ONLY from Germany) said yes?: 340 / 1000 

 

Of those who said yes, what proportion were from Germany?: 340/2175 

Segmented bar chart

Divides a bar proportionally into segments corresponding to the percentage in each group

How many variables are in this chart?: 2 

1) Gender 

2) What they watched 

How many categories?: 4 

1. Game 

2. Commercials 

3. Won't watch 

4. Don't know