L4 - Descriptive Statistics & Inferential Statistics

Descriptive Analytics

includes descriptive statistics but also involves data visualization and reporting to interpret past data and provide insights

Descriptive Analytics

- Data aggregation and summarization

- Visualizations (charts, graphs, heatmaps)

- Dashboards and reports

Descriptive Statistics

mathematical computations used to summarize and describe the characteristics of a dataset

Descriptive Statistics

speed up and simplify comprehension of a group's characteristics

Location

central value of the variable (the mean is the most common measure)

Variability

The spread of the data from the center value (i.e. variance, standard deviation)

Central Tendency

shows the center value in a dataset

mean

median

mode

Mean

Average value.

Imputation used if the data is symmetrical.

Median

Middle value.

Imputation used if there are outliers or data is asymmetrical

Mode

Most frequent.

Imputation used for categorical (qualitative) variables.

Variation

Summary of differences within group.

Range

Interquartile range

Standard deviation

Variance

Range

The difference between the highest and lowest values

Interquartile range

The range of the middle half of a distribution.

Q3 - Q1

25th - 75th percentile

Standard deviation

Average distance from the mean (sqrt of variance)

Variance

Average of squared distances(deviation) from the mean

Aggregation

_______ based on segment or time period

Population

The entire group of people or objects that share a common characteristic.

The total number of observations in a given group or context.

The number of people in a single area.

Sample

A smaller representative group drawn from the population.

A portion, part, or fraction of the whole group.

A subset of the population of interest.

Inferential Statistics Tools

They are commonly used for hypothesis testing, allowing you to draw conclusions about populations based on sample data.

T-Test

Used to determine if two means (or two groups) significantly differ from each other. Tells you how significant the differences between groups are. Lets you know if those differences (measured in means) could have happened by chance.

T-Test

1 predictor (2 categories or levels) (i.e., sex = male or female)

1 outcome (numerical

T-Test

Sample Problems Addressed:

- Does price sensitivity differ between those who earn 50k a month and those who earn 70k a month?

- Is there a gender difference in preference for Car A?

T-Test

Steps:

•Compute the effect (t value)

•Determine the statistical significance (p-value) of the effect

T-score

•a ratio between the difference between two groups and the difference within the groups

•a large ____ tells you that the groups are different

•a ____ of 3 means that the groups are three times as different from each other as they are within each other.

P-value

•the probability that the results from your sample data occurred by chance

•__________ are from 0% to 100%

•a _________ of less than 0.05 (5%) indicates that the data did not occur by chance.

a ________ of .01 means there is only a 1% probability that the results from an experiment happened by chance.

Independent Samples t-test

Compares the means for two independent groups.

Dependent Samples t-test (Paired sample t-test)

Compares means from the same group at different times (say, one year apart)

One sample t-test

A ________ tests the mean of a single group against a known mean.

Analysis of Variance

Comparing 3 or more Groups. Used to determine differences in means between 3 or more groups

Analysis of Variance

1 predictor (3 categories or levels) (i.e., promotion = tasting, decoration, or display)

1 outcome (numerical)

Analysis of Variance

Steps:

•Compute the overall effect (f value)

•Determine the statistical significance (p value) of the overall effect

•If the overall effect (F value) is significant, do a follow-up post- hoc mean comparison test.

Analysis of Variance

Sample Problems Addressed:

Does type of promo for a soup brand affect sales?

Is there a social class difference in taste preference?