Statistical Analysis in Layman’s View
What is Statistical Analysis? (Layman’s View)
Statistical Analysis = “Using Numbers to understand Reality and make Decisions.”
It’s like taking a messy Pile of Facts (Data) and turning it into Clear Stories.
Example:
Suppose you run a Juice Shop. You note:
•
•
•
•
Daily Sales
Temperature
Advertisement Spending
Day of Week
You want to answer:
•
•
•
•
“Do Hot Days bring More Sales?”
“Does Advertising increase Sales?”
“Which Days are Busiest?”
“How Much Stock to prepare Next Week?”
For this, you apply Different Types of Statistical Analyses, depending on your Question.
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Major Types of Statistical Analysis (Layman Concept)
Type
Descriptive
“What happened?”
Comparative / Inferential
“Are Groups different?”
Relationship / Correlation
Regression / Prediction
Group Differences with (ANOVA /
MANOVA)
Non-parametric Tests
Time Series
“Are Two Things connected?”
“Can I predict One Thing from Others?”
Layman Example
Average
Daily
Sales?
Highest
Temperature?
Are Sales Higher on Weekends vs
Weekdays?
Do Temperature and Sales rise Together?
Predict Sales from Temperature + Ads
“Do Multiple Conditions affect Outcome?”
Effect of Season & Ad Type on Sales
Chi-square / Association
Factor / PCA
Reliability / Validity
Advanced (Mediation / Moderation /
SEM)
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Main Question
“Can I test Without Strict Assumptions?”
“What happens Over Time?”
Small Sample, or Skewed Data
Sales Trend through the Year
Are Product Preference & Gender
“Are Two Categories linked?”
related?
“Can I reduce Complex Data to fewer Themes?”
Reduce 20 Survey Questions to 3 Factors
“Is my Measurement Tool Consistent and Correct?” Are my Survey Questions stable & clear?
“How do Variables influence Each Other
Ads → Brand liking → Sales
Indirectly?”
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Common Statistical Tests (Layman Description)
Analysis Type
Descriptive
Comparative
Relationship
Regression
Non-parametric
Categorical
Time Series
Factor Analysis
Reliability
Mediation /
Moderation
Test Name
Mean, Median, Mode, SD
t-test, ANOVA
Correlation (r)
Simple & Multiple Regression
Mann–Whitney, Kruskal–Wallis
Chi-Square
ARIMA, Trend analysis
EFA, PCA
Cronbach’s Alpha
Layman Meaning
Summarize the Data (Average, Typical, Variation)
Compare Two or More Groups (e.g., Male vs Female Scores)
See if Two Variables move Together
Build an Equation to Predict One Variable from Others
Same as t-test/ANOVA but for Non-Normal Data
Check if Two Categories are related (e.g., Yes / No Responses vs Gender)
See Patterns over time and forecast
Find Hidden Patterns / reduce Many Questions to themes
Check if a Questionnaire is consistent
Regression with Indirect Effects
Find Why or When Relationships happen
Layman Scenarios & Matching Analyses
Scenario
You want to know the Average Daily Sales
You want to check if Weekend Sales are Higher Than Weekdays
You want to check if Different Advertising Methods lead to Different Sales
You want to check if Temperature & Sales are linked
You want to Predict Sales using Temperature + Ads
You want to see if Product Preference Differs by Gender
You want to check Sales Trends across 12 Months
You collected a Survey with 20 Items and want to Group Similar Questions
You want to ensure your Survey is Reliable
You suspect ads increase Brand Liking, which then increases Sales
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Statistical Analysis
Descriptive Stats (Mean, SD)
t-test
One-way ANOVA
Correlation
Multiple Regression
Chi-square Test
Time Series / Trend Analysis
Factor Analysis
Cronbach’s Alpha
Mediation Analysis
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Why These Analyses Matter
Without Statistics
With Statistics
Guesswork
Evidence-based
“I think Hot Days bring More Sales.” “The Correlation between Temperature & Sales is 0.95.”
“Maybe Our New Ad worked.”
“ANOVA shows a Significant difference between Ad Types (p < .01).”
“Hope Sales grow Next Month.”
“Time Series Forecast predicts a 15% increase Next Month.”
Simple Rule to Choose Analysis
Ask Yourself:
1.
What is my Question?
2.
What is my Data Type (Number, Category, Time)?
3.
How many Groups / Variables are involved?
4.
Am I Describing, Comparing, finding Relationships, or Predicting?
This guides you to the Right Test.
Example:
“Does Advertising Method affect Sales differently on Weekdays vs Weekends?”
•
•
2 Factors → Ad Type (A/B/C) & Day Type (Weekday / Weekend)
Outcome: Sales (Numeric)
Two-way ANOVA
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Key Takeaway (Layman Summary)
Descriptive → Tell me the Story of the Data.
• Comparative → Are Groups different?
• Relationship → Do Variables move Together?
• Regression → Can I predict Something?
• ANOVA / Chi-Square → Do Different Factors influence Outcomes?
• Advanced Methods → Dig deeper into “How” and “Why.”
Think of these like Different Tools in a Toolbox
— You pick the tool depending on the job.
•
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👉 MULTIVARIATE ANALYSIS
Don’t worry, I’ll explain it from a Layman’s Perspective with Simple Examples
What is Multivariate Analysis? (Layman’s Definition)
Multivariate Analysis = analyzing More Than One Variable at the Same Time to understand Complex Real-World Patterns.
“Multi” = many
• “Variate” = variables
Simple Example:
You run a juice shop
again.
You have data on each day:
•
Temperature
•
Advertising spend
•
Customer footfall
•
Day of the week
•
Total Sales
Instead of studying Each Factor Separately, Multivariate Analysis lets you study all of them Together — because in real life,
Many Factors Work at the Same Time.
•
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Why Multivariate Analysis is Needed (Layman)
Imagine you want to understand what drives your Sales:
•
•
•
•
Hotter Days → More Sales
More Advertising → More Sales
Weekends → More Customers
Maybe Some Combinations work Better than Others
If you look at these One by One, you might get confused:
•
A Hot Weekday with No Ads vs. a Cooler Weekend with Ads — which matters more?
Multivariate Analysis solves this by analyzing Multiple Relationships at once
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Main Types of Multivariate Analysis (Layman Summary)
Multivariate Technique
Multiple Regression
Multivariate Analysis of
Variance (MANOVA)
Factor Analysis / PCA
Layman Purpose
Predict One Variable using Several
Predictors
Compare Groups on Several
Outcome Variables Simultaneously
Reduce Many Variables into fewer
Underlying Factors
Cluster Analysis
Group Similar Cases into Clusters
Discriminant Analysis
Predict Group Membership using
Several Variables
Canonical Correlation
Multivariate Time Series /
Panel Data
Structural Equation
Modeling (SEM)
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Study Relationship between Two Sets
of Variables
Analyze Multiple Time-Dependent
Variables Together
Study Complex Cause–Effect Models
with Multiple Variables
Example Scenario
Predict Juice Sales using Temperature + Ads + Weekend
Compare Male & Female Customers on both Spending and
Satisfaction
Reduce 20 Survey Questions into 3 Main Themes (Taste,
Service, Price)
Group Customers into “Daily buyers”, “Weekend Buyers”,
“Tourists”
Predict whether a Customer belongs to “High-Spender” or
“Low-Spender” group based on Age, Income, and Visit
Frequency
Relationship between (Price, Ads, Location) and (Sales,
Satisfaction, Loyalty)
Study Temperature, Ad Spend & Sales Trends together Over
12 Months
Ads → Brand liking → Loyalty → Sales (with Direct &
Indirect Paths)
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Layman Scenarios and Matching Multivariate Methods
Layman Question
“Can I predict Sales using Many Factors together?”
“Do Different Ad Types affect both Sales and Customer Satisfaction?”
“I have 30 Survey Questions — can I find the Main Themes?”
“Can I group my Customers into Natural Segments?”
“Can I classify Customers into High / Low Loyalty Groups using Several Traits?”
“How are Marketing Strategies (Price, Ad, Discount) related to Customer Responses
(Sales, Loyalty, Feedback)?”
“How do Multiple Variables interact Over Time?”
“What are the Direct and Indirect Effects in My Model?”
Best Technique
Multiple Regression
MANOVA
Factor Analysis / PCA
Cluster Analysis
Discriminant Analysis
Canonical Correlation
Multivariate Time Series
SEM (Structural Equation Modelling)
Simple Layman Examples
Example 1: Multiple Regression
Predict Sales using Temperature, Advertising, and Number of Walk-ins.
→ You get an equation that uses All Three Together to make a More Accurate Prediction.
Example 2: MANOVA
You compare Two Types of Advertising Campaigns (Online vs Offline).
You measure Sales and Customer Satisfaction.
→ MANOVA checks if there’s a Combined Difference across Multiple Outcomes, not just one.
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Example 3: Factor Analysis
You give a 20-Question Survey about Customer Experience.
Instead of analyzing 20 Separate Questions, Factor Analysis Groups them into:
Factor 1: Taste Quality
• Factor 2: Service
• Factor 3: Price Perception
→ Now you can work with 3 Themes Instead of 20 Items.
•
Example 4: Cluster Analysis
You look at Customer Purchase Patterns.
Cluster analysis Groups them Automatically into:
• Group A: “Daily Buyers”
• Group B: “Weekend Family Shoppers”
• Group C: “Tourists (High Spend, Rare Visits)”
→ You can market differently to Each Group.
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Key Layman Ideas Behind Multivariate Analysis
Concept
Layman Explanation
Multiple variables together Real Life is Complex — Many Factors influence Outcomes simultaneously.
Hidden patterns
Multivariate Methods can find themes or Groups you may not see with Simple Analysis.
Efficiency
You avoid Repeating Many One-Variable Tests and get a Full Picture at once.
Marketing, Education, Health, Business — all Benefit from seeing the “Whole System,”
Better decisions
not just One Piece.
Quick Layman Summary Table
Type
What it Does
Layman Example
Multiple Regression
Predict One Variable Using Many Others
Predict Sales using Temp, Ads, Day
MANOVA
Compare Groups Across Several Outcomes Compare Ad Types on Sales + Satisfaction
Factor Analysis
Reduce Many Variables to Fewer Factors
20 Survey Items → 3 Key themes
Cluster Analysis
Group similar People or Items
Find 3 Customer Types
Discriminant Analysis Classify into Groups
Predict High vs Low Spenders
Canonical Correlation Link Two Sets of Variables
Marketing Strategies ↔ Customer Reactions
SEM
Complex Causal Models
Ads → Brand → Loyalty → Sales
Key Takeaway (Layman)
Multivariate Analysis is like watching the Whole Orchestra
instead of just One Instrument
You see how all the pieces Work Together, not separately.
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Simple Linear Regression Analysis
The meaning of r, R², Coefficient, and Error — using a Very Simple, Real-Life Example
Imagine this Situation:
You run a Small Juice Shop.
You want to find out:
“Does Temperature affect my Sales of Juice?”
So, for 10 days, you note:
•
The Temperature Each Day
(in °C)
•
How Many Cups of Juice you sell
Day Temperature (°C) Juice Sold (Cups)
1
25
40
2
28
45
3
30
52
4
32
58
5
35
70
6
36
72
7
34
65
8
31
55
9
29
50
10
27
43
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Run a Simple Linear Regression
Juice Sales = a + b × Temperature
1. r (Correlation Coefficient)
r tells how strongly Two Variables are related.
• Value Ranges from –1 to +1:
o +1 = Perfect Positive Relationship
o 0 = No Relationship
o –1 = Perfect Negative Relationship
In Our Example, as Temperature goes up, Sales also go up.
So r ≈ +0.95 (Very Strong Positive Relationship).
•
Layman meaning: “When the Weather is Hotter, People usually buy More Juice — Almost Always.”
2. R² (Coefficient of Determination)
•
R² tells How Much of the Variation in Sales can be explained by Temperature.
•
It ranges from 0 to 1 (or 0% to 100%).
Here, R² ≈ 0.90, meaning:
“90% of the Changes in Juice Sales are explained by Temperature.”
Layman meaning: “If you know the Temperature, you can predict Sales with 90% Accuracy.”
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3. Coefficient (b)
This is the slope in the Regression Equation:
Sales = a + b × Temperature
Suppose you get:
Sales = –20 + 2.5 × Temperature
•
Here:
o
a = –20 → the Intercept (Sales when Temperature = 0°C, just for Calculation)
o
b = 2.5 → the Coefficient
Layman meaning: “For every 1°C increase in Temperature, juice Sales increase by about 2.5 Cups.”
Example: At 30°C → Predicted Sales = –20 + 2.5×30 = 55 CUPS
4. Error (Residual)
•
Error = Actual Sales – Predicted Sales
•
It shows How Far the Prediction was from Reality.
Example: On Day 3 (Temp = 30°C),
•
Predicted Sales = 55 Cups
•
Actual Sales = 52 Cups
Error = –3 Cups (Model Predicted Slightly Higher than Actual).
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Layman meaning: “Sometimes Your Guess is a bit off — that Difference is called Error.”
In Regression, we try to minimize these Errors Overall.
Summary Table
Term
Technical Meaning
Layman Meaning
R
Correlation between X and Y
Strength of the Relationship
R²
% of Y explained by X
How Well the Model Fits Overall
Coefficient (b) Change in Y for each One Unit Change in X Slope — How Much Y moves when X changes
Error
Actual – Predicted
Difference between Real and Guessed Value
Final Simple Example
“If Today’s Temperature is 33°C, My Model predicts:
Sales = –20 + 2.5×33 = 62.5 cups.”
Actual Sales might be 60 or 65 → that Small Difference is Error.
If r = 0.95 and R² = 0.90, you can trust your Prediction quite well.
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Let’s continue the same “Temperature → Juice Sales” Regression Example, but now see it as if you had run the Analysis in Excel or
SPSS or JAMOVI.
Excel Regression Output
Suppose you ran:
Data → Data Analysis → Regression
(Dependent Variable = Juice Sales, Independent Variable = Temperature)
You might get a Table like this:
Regression Statistics
Statistic
Value
Multiple R
0.9498
R Square
0.9022
Adjusted R Square 0.8899
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Standard Error
2.98
Observations
10
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Interpretation:
•
Multiple R = 0.9498 →
This is r, a Very Strong Positive Correlation between Temperature and Sales.
•
R Square = 0.9022 →
90.2% of the Variation in Juice Sales is explained by Temperature.
•
Adjusted R² = 0.8899 →
Adjusted for Number of Predictors (important for Multiple Regression, but here Only One Predictor).
•
Standard Error = 2.98 →
On Average, the Model’s Predictions are off by about 3 Cups.
ANOVA Table
Source
Regression
Residual
Total
df
SS
MS
F
Significance F
1 978.2 978.2 110.2
0.0000001
8 71.0
8.88
9 1049.2
Interpretation:
•
F = 110.2, p < 0.0001 →
The Regression is statistically Significant — Temperature is Indeed a Good Predictor of Sales.
Coefficients Table
Variable
Coefficient Standard Error t Stat P-value
Lower 95% Upper 95%
Intercept
–20.00
5.30
–3.77 0.0054
–32.8
–7.2
Temperature 2.50
0.24
10.50 0.0000001 1.96
3.04
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Interpretation:
•
Intercept (–20.00) → When Temperature = 0, Predicted Sales = –20 (Theoretical Starting Point).
•
Temperature (2.50) → For each 1°C Increase, Sales go up by 2.5 Cups.
•
P-value for Temperature = 0.0000001 → very significant (Strong Evidence the Relationship is Real).
JAMOVI Output Example
If you use Jamovi:
•
Go to Regression → Linear Regression
•
DV: Juice Sales
•
IV: Temperature
You might see something like this
Model Fit Measures
Model R
R² Adjusted R² RMSE
1
.950 .902 .890
2.98
Interpretation is the same as Excel’s “Regression Statistics”.
Model Coefficients
Predictor Estimate SE
t
P
95% CI
Intercept
–20.00 5.30 –3.77 0.0054 [–32.8, –7.2]
Temperature
2.50
0.24 10.50 <.001 [1.96, 3.04]
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Same interpretation:
•
•
•
Estimate = Coefficient
SE = Standard Error of the estimate
t & p = test whether the coefficient is significantly different from 0
Residuals Plot
Jamovi (and Excel if you insert chart) often gives a scatter plot and residual plot:
•
Scatter Plot: Temperature vs Sales + Fitted Regression Line
•
Residual Plot: Errors should be scattered Randomly (no pattern) — indicates a Good Fit.
Final Layman Recap
Term
r (Multiple R)
R²
Coefficient
Error (Residual)
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Where You See It
Excel: Regression Statistics / Jamovi: R
Same Section
Coefficients Table
Residual Plots / Std. Error / RMSE
What It Tells You (Simple)
How Strongly Two Variables move Together
How Much of the Outcome is explained by the Predictor
How Much the Outcome changes when Predictor changes
How Far the Prediction is from Reality
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Multiple Regression Analysis
Imagine this Situation:
You own a Juice Shop again
But this time, you realize Temperature is not the only Thing affecting juice Sales.
You think Two Factors might influence Daily Sales:
1.
Temperature (in °C)
2.
Advertising Spend (in ₹ per day for Posters / Offers)
Your question is:
“Can I predict Daily Juice Sales using both Temperature and Advertising together?”
Collected Data (10 Days)
Day Temperature (°C) Advertising (₹) Juice Sold (cups)
1
25
100
45
2
28
200
55
3
30
150
60
4
32
300
75
5
35
250
85
6
36
400
95
7
34
300
80
8
31
200
65
9
29
150
58
10
27
100
48
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Step 1: Run Multiple Regression
Regression Model: Juice Sales = 𝑎 + 𝑏1 × Temperature + 𝑏2 × Advertising
You can run this in Excel:
•
Go to Data → Data Analysis → Regression
•
Select Y Range = Juice Sold
•
Select X Range = Temperature and Advertising Columns
Step 2: Sample Excel Output
Regression Statistics
Statistic
Multiple R
R Square
Adjusted R²
Standard Error
Observations
Value
0.9830
0.9663
0.9566
3.12
10
Interpretation:
•
R = 0.983 → Strong Combined Relationship between Predictors (Temperature + Advertising) and Sales.
•
R² = 0.9663 (96.6%) → 96.6% of the Variation in Juice Sales is explained by Temperature & Advertising Together.
•
Adjusted R² = 0.9566 → Adjusted for Number of Predictors (Important when you have more than One X).
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Coefficients Table
Variable Coefficient Std Error t Stat P-value
Intercept
–30.00
5.8
–5.17 0.0011
Temperature
2.00
0.30
6.67 0.0002
Advertising
0.10
0.02
5.00 0.0015
Interpretation:
•
Intercept (–30)
Theoretical starting Sales when both Temperature & Advertising = 0 (Not Realistic, just part of formula).
•
Temperature coefficient (2.00)
For Every 1°C increase in Temperature, Sales Increase by 2 Cups, keeping Advertising Constant.
•
Advertising coefficient (0.10)
For every ₹1 spent on ads, Sales Increase by 0.1 Cup, keeping Temperature Constant.
So ₹100 more Ads = 10 more Cups!
•
Both P-Values < 0.05 → Both Predictors are statistically Significant.
Step 3: Prediction Example
Let’s say Tomorrow:
• Temperature = 33°C
• Advertising = ₹300
Prediction using Model:
Sales = −30 + (2.00 × 33) + (0.10 × 300)
Sales = −30 + 66 + 30 = 66 cups
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Layman meaning:
If it’s 33°C and you spend ₹300 on Ads, you can expect to sell about 66 Cups of Juice Tomorrow.
Step 4: Key Terms Explained
Term
Multiple
Regression
Coefficient
R²
Adjusted R²
P-Value
Prediction
Meaning
Layman Example
Predicting Y using Two or More X Variables
Predict Sales using Temperature + Advertising
Effect of Each Predictor on Y, keeping Others Constant
Temperature ↑ 1°C → Sales ↑ 2 Cups; Ads ↑ ₹100 → Sales
↑ 10 cups
% of Variation in Y explained by All Predictors
Together
R² Adjusted for Number of Predictors
Tests if Predictor is significant
Use the Regression Formula to estimate Future Values
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96.6% of Sales Variation is explained
More Accurate Measure when Multiple X’s
Both Temp & Ads are statistically Important
Tomorrow’s Sales estimate = 66 Cups
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Layman Analogy
Think of Multiple Regression like making Juice with Two Ingredients
+
:
Temperature =
• Advertising =
• Sales =
Using only one fruit (temperature) gives a good taste.
But when you Combine Both Fruits (temperature + ads), the juice (Sales prediction) becomes Richer & More Accurate
•
Why Multiple Regression is Useful
•
Real-World Outcomes are rarely affected by Just One Factor.
•
Multiple Regression lets you understand the Separate and Combined Impact of Many Factors at Once.
•
It helps you decide where to focus:
o
If Advertising Coefficient is very small → Spending More on Ads may not be Effective.
o
If Temperature is Big → maybe plan More Stock for Hot Days.
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