Ch 5- Types of Data Analysis

descriptive analytics

characterizes, summarizes, and organizes features and properties of the data to facilitate understanding of the results and the underlying data

what happened/what is happening

sources for descriptive analysis

financial statements

internal information systems

external sources

statistical and summarization tools for descriptive analysis

counts

totals, sums, averages, subtotals

min, max, medians, standard deviation

graphs, bar charts, histograms

horizontal and vertical analysis

ratio analysis

diagnostic analysis

performed to investigate the underlying cause that cannot be answered by simply looing at the descriptive data

why did it happen

what are the reasons for the past result

can we explain why it happened

identify anomalies/outliers

unusual/unexpected results or transactions

Benford’s law

Benford’s law

in any large, randomly produced set of natural numbers, there is an expected distribution of the first digit

if a distribution departs from the expectation it is considered an anomaly and should be investigated

finding previously unknown linkages, patterns, or relationships

drill-down analysis

determine relations/patterns/linkages between varaibles

drill-down analysis

used to uncover details in the data by looking at difference levels of the data to understand why something happened

look for patterns to identify potential correlations

determine relations/patterns/linkages between varaibles

correlation

regression

hypothesis testing

predictive analysis

performed to foresight by identifying patterns in historical data and assessing the likelihood or probability

will it happen in the future

what is the probability something will happen

is it forecastable

3 broad categories of predictive analysis

classification

regression

forecasting using time series analysis

prescriptive analysis

performed to identify the best possible options given constraints or changing conditions

what should we do based on what we expect to happen

how do we optimize our performance based on potential contraints

5 broad categories of prescriptive analysis

sensitivity

capital

marginal

goal-seeking

what-if scenario

sensitivity analysis

evaluate outcomes based on uncertainty regarding the inputs

capital analysis

evaluating future cash flows for potential investments

marginal analysis

used to determine the change in profit association with the cost or benefit of the next unit produced

goal-seeking analysis

what-if analysis that tells what needs to be done to reach a desired outcome

what-if scenario analysis

analysis of potential future events by considering potential outcomes

population

group of phenomenon having something in common

sample

a subset of members of a population selected to represent that population

parameter

characteristics of a population

statistic

characteristic of a sample

mean

sum of all data points divided by the number of data points

median

midpoint of the data in a sorted array

mode

observation that occurs most frequently

range

differences between the maximum and minimum values

variance

average of squared differences from the mean

standard deviation

square root of the variance

probability distributions

statistical property that describes the possible values of random variables and the likelihood that a random variable will be within a given range

3 primary probability distributions

normal

uniform

poisson

normal distribution

bell-shaped probability distribution that is symmetric about the mean with data points closer to the mean frequent than those farther from the mean

how much data is included when data is within 1 sd

68%

how much data is included when data is within 2 sd

95%

how much data is included when data is within 3 sd

99.7%

z-score

tells how many standard deviations a data point is from the mean

uniform distribution

probability distribution where all outcomes are equally likely

poisson distribution

distribution characterized as the mean number of events per interval of space or time

hypothesis

assumption of theory based on an understanding of the data

null hypothesis

assumes that the hypothesized relationship does not exist; there is no significant difference between two samples or populations

H₀

grades for students who study are less than or equal to the grades for students who do not study

alternate hypothesis

the case that is believed to be true; opposite of the null hypothesis or a result that is expected

H_A

grades for students who study are greater than grades for students who do not study

p-value

result of a test that either rejects or fails to reject the null hypothesis

determine statistical significance by comparing the p-value to a threshold value

p-value > threshold

fail to reject the null hypothesis; not significant result

p-value less than or equal to threshold

reject the null hypothesis; significant result

confidence interval

measures the probability that a population parameter will fall between two set values

sample t-test

used to compare the means of two sets of data observations

paired t-test

compares the same population but at a different time

statistical output from a regression

used to measure the relationship between one output variable and various inputs

output variables

dependent variable

input variable

independent variable