In doomlab/learnSTATS: Introduction to Statistics (ANLY 500)

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Welcome to ANLY - 500

• ANLY 500 will focus on the foundations of:

  • Data Analytics,
  • Research Methodology, and
  • R programming Language.

• The first question we must ask ourselves in this course is: What is Analytics?

• We should note analytics can be defined in two ways!

What is Analytics? - Possible Definition 1

• The utilization of:

  • data,
  • information technologies (R software, Python, SAS, etc.)
  • statistical analysis
  • quantitative and qualitative methods,
  • mathematical or computer based models to help decision making through improved insights.

What is Analytics? - Possible Definition 2

• It is considered the process of examining data to draw conclusions about the information contained
• Which is improved/expanded with the aid of specialized software.

Scope of Analytics?

• The focus of data analytics can be defined under three scopes, including:

  • (1) Descriptive Analytics
  • (2) Predictive Analytics
  • (3) Prescriptive Analytics

What is Descriptive Analytics? (1)

• Definition - the use of data to understand past and current business performance and make informed decisions.
• We are asking what happened?

knitr::include_graphics("pictures/introDA1/descriptive.png")

An Example of what to Expect in Descriptive Analytics: Ex.1.1

• Dataset: "Sunspot Trends from 1749-01-01 to 2013-09-01'"

• Description: Understand the Historical Trend of Sunspots from 1749 to 2013.

  • Notice, we're accessing data.
  • Here we use the datasets package available in R:

library(datasets) 
data("sunspot.month") # special way to load embedded data
head(sunspot.month)

An Example of what to Expect in Descriptive Analytics: Ex.1.1

• Understand the datasets structure & data types:

str(sunspot.month)

An Example of what to Expect in Descriptive Analytics: Ex.1.1

• Get Basic Stats from the dataset:
• Here, will get some basic summary stats to better understand the data.

summary(sunspot.month)

An Example of what to Expect in Descriptive Analytics: Ex.1.1

• Visualize the trend of the dependent variable from the dataset:
• Here, will visualize the data to better understand the sunspots historical trend from 1749 to 2013.
• In a few weeks, we will cover how to make these plots!

library(ggplot2)
sunspot.month <- as.data.frame(sunspot.month)
sunspot.month$Time <- 1:nrow(sunspot.month)
ggplot(sunspot.month, aes(x = Time, y = x)) + 
  geom_point(alpha = 0.5) + 
  ylab("Number of Sunspots") + 
  xlab("Time") +
  theme_classic()

What is Predictive Analytics?

• Definition - predict the future by examining historical data, detecting patterns or relationships in the data, and then extrapolating these relationships forward in time.
• We are asking what could happen?

knitr::include_graphics("pictures/introDA1/predictive.png")

What is Predictive Analytics?

• On the next slide is a simple example of a predictive model using a simple/multiple linear regression model.
• By the end of the course you'll be able to build a linear model and interpret the results from this simple example.

An Example of what to Expect in Predictive Analytics: Ex.2.1

• Let's import some data from the quantmod package.
• Provides access to both stock data, but also useful functions for stock analysis.
• Understand the Data Structure and Data Types:

library(quantmod)
start <- as.Date(Sys.Date()-(365*5))
end <- as.Date(Sys.Date()-2)
getSymbols("AMZN", src = "yahoo", from = start, to = end)
str(AMZN)

An Example of what to Expect in Predictive Analytics: Ex.2.1

• Build a Model:

predictive_model <- lm(formula = AMZN.Close ~ AMZN.High + AMZN.Low + AMZN.Volume, 
                       data = AMZN[1:1199,])
summary(predictive_model)

An Example of what to Expect in Predictive Analytics: Ex.2.1

• Visualize the Models Performance:

par(mfrow=c(2,3))
plot(predictive_model,1)
plot(predictive_model,2)
plot(predictive_model,3)
plot(predictive_model,4)
plot(predictive_model,5)

An Example of what to Expect Analytics: Ex.2.1

• Make a Prediction:

n <- length(AMZN[,1])
prediction <- stats::predict(predictive_model, AMZN[1200:n,])
tail(data.frame(prediction))

An Example of what to Expect Analytics: Ex.2.1

• Make a Prediction:

plot(prediction, type = "l")

What is Prescriptive Analytics?

• Definition - identify the best alternatives to minimize or maximize some objective.
• We are asking what should we do?
• Optimization is a recommendation!

knitr::include_graphics("pictures/introDA1/prescriptive.png")

What does this translate into?

• Analytics is the discovery, interpretation and communication of meaningful patterns or summary of data using data analytics.

  • Note that Analytics is a mindset and Data Analytics is a process.
  • So conducting analytical research is based on a way of thinking and acting on data.

• Now we should be asking the question: What is Data Analytics?

What is Data Analytics?

• It is the process of examining data sets in order to draw conclusions about the information it contains.
• The question we should be asking now, is: How to perform data analytics?

A Subcomponent of Data Analytics is Data Analysis!

• Data Analytics is a broad term that includes data analysis as a necessary subcomponent.
• In other words analytics defines the science behind analysis.

A Subcomponent of Data Analytics is Data Analysis!

• High level analysis techniques commonly used in data analytics include:

  • Exploratory Data Analysis (EDA): which aims to find patterns and relationships in data.
  • Confirmatory Data Analysis (CDA): which applies statistical techniques to determine whether hypotheses about a data set are true or false.

• However, two other types of analysis may be considered.

Other Types of Analysis

• Quantitative data analysis: involves analysis of numerical data with quantifiable variables that can be compared or measured statistically.

  • Testing theories using numbers.

• Qualitative data analysis: it is more interpretive. It focuses on understanding the content of non-numerical data like text, images, audio and video, including common phrases, themes and points of view.

  • Testing theories using language.

How to Correctly Apply Data Analytics?

• The Research Process should be used to conduct either quantitative or qualitative data analysis:

knitr::include_graphics("pictures/introDA1/research_process.png")

Breaking Down the Research Process - The Initial Observation

• Find something that needs explaining.

knitr::include_graphics("pictures/introDA1/initial_obs.png")

Breaking Down the Research Process - The Initial Observation

• In other words, formulate a question that needs to be answered.

  • Observe the real world
  • Read other research
  • Ask others about the problem

Breaking Down the Research Process - The Initial Observation

• Test the concept:

  • Collect data to see whether your hunch is correct.
  • To do this you need to define variables.
  • Variables are anything that can be measured and can differ across entities or time.

Breaking Down the Research Process - Generating Theories

• Theory:

  • Definition - A hypothesized general principle or set of principles that explains known findings about a topic and from which new hypotheses can be generated.

knitr::include_graphics("pictures/introDA1/cartoon_theory.png")

Breaking Down the Research Process - Creating a Hypothesis

• Hypothesis:

  • Definition - A prediction from a theory.
  • Should be clear and understandable
  • Should be testable
  • Should be measurable

Breaking Down the Research Process - Testing Theories & Hypotheses

• Falsification:

  • Definition - The act of disproving a theory or hypothesis.

knitr::include_graphics("pictures/introDA1/kp_false.png")

Breaking Down the Research Process - Identifying the Variables

• Independent Variable:

  • The proposed cause
  • A predictor variable
  • A manipulated variable (in experiments)

• Dependent Variable:

  • The proposed effect
  • An outcome variable
  • Measured not manipulated (in experiments)

What's After the Question & Identifying Variables?

• An important element of analyzing the data is the different levels of measurement to consider.
• Note we should be asking ourselves a question: What exactly is data?

What is Data?

• Data is a set of values/measurements of quantitative or qualitative variables.

  • It is information in a raw or unstructured form.
  • It can consist of fact, figure, characters, symbols, etc.

Types of Measurements

• In a dataset, we can distinguish two types of variables:

  • (1) Categorical and,
  • (2) Continuous.

Categorical Variables

• Definition - entities that are divided into distinct categories.

• Includes the following:

  • Binary variables
  • Nominal variables
  • Ordinal variables

• R stores categorical variables as a factor or character.

• Factors are the variables in R which take on a limited number of different values.

Categorical Levels of Measurement - Binary

• Definition - a binary variable is only two categories.

  • Dead or alive
  • On or off

Categorical Levels of Measurement - Nominal

• Definition - A nominal variable is more than two categories.

• Whether someone is an Assistant, Associate, or Full Professor.

Categorical Levels of Measurement - Ordinal

• Definition - A ordinal variable is the same as a nominal, but the categories have a logical order.

  • Whether people got a fail, a pass, a merit or a distinction in their exam.
  • If you classify economic status, with three categories (low, medium and high).

• In addition to being able to classify values into categories, you can order the categories: first, second, third

Continuous Variables

• Definition - entities get a distinct score.

• Includes the following:

  • Interval variables
  • Ratio variables

Continuous Levels of Measurement - Interval

• Definition - A interval variable is equal intervals on the variable. It represents equal differences in the property being measured. This variable also does not have a true zero.

  • i.e. The difference between 6 and 8 is equivalent to the difference between 13 and 15.
  • i.e. Temperature of zero does not represent an lack of temperature

Continuous Levels of Measurement - Ratio

• Definition - A ratio variable is the same as an interval variable, but the ratios of scores on the scale must also make sense. This variable does have a true zero.

  • i.e. A score of 16 on an anxiety scale means that the person is, in reality, twice as anxious as someone scoring 8.

Consider Measurement Error:

• The accuracy of the measurements are key to your solutions.

• Measurement Error: - aka observational error

  • Definition - The discrepancy between the actual value we're trying to measure, and the number we use to represent that value.

    • i.e. You (in reality) weigh 80 kg.
    • i.e. You stand on your bathroom scales and they say 83 kg.
    • i.e. The measurement error is 3 kg.

How Valid Are My Measures?

• Validity:

  • Definition - Whether an instrument measures what it set out to measure.

• Including the following:

  • Content validity - Evidence that the content of a test corresponds to the content of the construct it was designed to cover.
  • Ecological validity - Evidence that the study, experiment or test can be applied, and allow inferences, to real-world conditions.

Are My Measures Reliable?

• Reliability:

  • Definition - The ability of the measure to produce the same results under the same conditions.

• Test-Retest Reliability:

  • Definition - The ability of a measure to produce consistent results when the same entities are tested at two different points in time.

Breaking Down the Research Process - Collecting the Data

• To use measures in any research and test them we must now understand the following: How to Measure?

• It is different for certain types of research, including:

  • Cross-sectional research
  • Longitudinal research
  • Correlational research
  • Experimental research

Cross-Sectional Research

• Definition - This term implies that data come from people at different age points, with different people representing each age point.

knitr::include_graphics("pictures/introDA1/cross_sectional_research_study.png")

Longitudinal Research

• Definition: Research wherein the sample people are tested at different time points over their lives.

Correlational Research

• Definition - Observing what naturally goes on in the world without directly interfering with it.
• Careful not to mix correlational research with correlation as a statistical analysis

Experimental Research

• Definition - One or more variables is systematically manipulated to see their effect (alone or in combination) on an outcome variable.

  • Statements can be made about cause and effect.

Experimental Research - Methods

• Cause and Effect (Hume, 1748)

  • 1. Cause and effect must occur close together in time (contiguity).
  • 1. The cause must occur before an effect does.
  • 1. The effect should never occur without the presence of the cause.

Experimental Research - Methods

• Confounding variables: the 'Tertium Quid'

  • A variable (that we may or may not have measured) other than the predictor variables that potentially affects an outcome variable.
  • The relationship between ice cream sales and accidental drowning is confounded by the weather.

Experimental Research - Methods

• Ruling out confounds (Mill, 1865)

  • An effect should be present when the cause is present and that when the cause is absent the effect should be absent also.
  • Control conditions: the cause is absent.

Breaking Down the Research Process - Methods to Collect the Data

• Considering the what & how to measure, we must now look at the methods of data collection.

• For instance:

  • Between-group/between-subject/independent

    • Different entities in experimental conditions

  • Repeated-measures (within-subject)

    • The same entities take part in all experimental conditions.
    • Economical
    • Practice effects
    • Fatigue

Types of Variation in the Data to Consider:

• Systematic Variation

  • Definition - Differences in performance created by a specific experimental manipulation.

• Unsystematic Variation

  • Definition - Differences in performance created by unknown factors

• Randomization

  • Definition - random selection or assignment equalizes unsystematic variation in the study.

Breaking Down the Research Process - Analyzing the Data

• The final piece to the research process is to analyze the data, which consists of graphing and fitting the data to a model.
• However, to properly analyze the data you need to consider some conditions.

Population vs Sample

• First, populations and samples should be understood so that your analysis is not misleading when interpreting results.

• Population

  • Definition - the collection of units (be they people, plankton, plants, cities, suicidal authors, etc.) to which we want to generalize a set of findings or a statistical model.

• Sample

  • Definition - A smaller (but hopefully representative) collection of units from a population used to determine truths about that population.

Fitting Models

• A simple statistical model can be used to analyze data.

  • We use a statistical model to represent what is happening in the real world.

• For instance, the mean is a hypothetical value.

  • It doesn't have to be a value that actually exists in the data set.
  • As such, the mean is simple statistical model.

Fitting Models

• For Example: The average sepal length of a flower in the iris dataset reflects such a value.

tapply(iris$Sepal.Length, iris$Species, mean)

Statistical Modeling Parameters

• Parameters of population statistics and sample statistics.

• Numbers estimated from the entire dataset is a representation of the population.

  • The numbers estimated from a single test/study/experiment are considered a sample.

  • Parameters = Greek Symbols

  • Statistics = Latin Letters

Statistical Modeling Parameters

• For Example: The mean of a flowers sepal length before gave us the population, but watch it changes as we randomly sample.

sample <- iris[sample(nrow(iris), 15), ]
tapply(sample$Sepal.Length, sample$Species, mean) #sample
tapply(iris$Sepal.Length, iris$Species, mean) #population

Applicable Statistical Models

• To analyze the data and generate interpretable results the following statistical models can be used:

  • Frequency distribution, measures of shape
  • Central tendencies, measures of distance
  • Dispersion, measures of spread
  • Going beyond the data with z-scores and association.

Summary

• In this lecture, you have learned:

  • An introduction to data analytics
  • Theories and hypotheses
  • Measurement of variables
  • Types of variables
  • Types of research design
  • Issues and considerations for data analysis

doomlab/learnSTATS documentation built on June 9, 2022, 12:54 a.m.