CAP 2.2: Statistical Test Types (REVISE) Flashcards

Question 1

Q

What is an unpaired T-test? What is its non-parametric equivalent?

Answer

A

📊** Unpaired (Independent) t-Test**

An unpaired t-test compares the means of two independent groups to see if they are significantly different.

It answers:

“Are the averages in these two unrelated groups different?”

🧠** When Do You Use It?**

Two independent groups
Continuous data
Approximately normally distributed
Similar variance

🏥** Clinical Examples**
1️⃣ Antidepressant Study

Compare mean depression scores between:

Drug group

Placebo group

2️⃣ Blood Pressure Comparison

Compare average systolic BP between:

Smokers

Non-smokers

🧠** Memory Hook (Unpaired t-test)**

Unpaired = Unrelated groups.

Or:

“Two groups. Two means. Test the difference.”

🔄 Mann–Whitney U Test (Non-Parametric Version)

The Mann–Whitney U test is the non-parametric alternative to the unpaired t-test, used when the data are not normally distributed or are ordinal. Instead of comparing means, it compares the ranked positions of values between two independent groups.

It answers:

“Are the values in one group generally higher or lower than the other?”

🔁 How It Relates to the t-Test

Unpaired t-test → compares means (assumes normal distribution)

Mann–Whitney U → compares ranks (no normality assumption)

Same situation (two independent groups),
different method when assumptions fail.

🧠** Better Memory Hook (Logical + Funny)**

“When the data get weird, call Mann–Whitney.”

Or even better:

t-test tests the Mean.
Mann–Whitney minds the Mess.

Because when the data are messy (skewed, non-normal), Mann–Whitney steps in.

🔥** Ultra-Exam Hook**
Unpaired t-test = Mean vs Mean
Mann–Whitney = Rank vs Rank

Question 2

Q

Provide a clinical example of data you would use a Mann-Whitney U test for?

Answer

A

Here’s a clear, exam-style clinical example of when and how a Mann–Whitney U test is used.

🔹 Clinical Scenario

A psychiatry registrar wants to compare depression severity scores between:

Group A: Patients treated with CBT
Group B: Patients treated with supportive therapy

Outcome measure: PHQ-9 score at 12 weeks

However:

The sample size is small (n = 12 per group)
The data are not normally distributed
Scores are skewed (some patients have very high scores)

Because the data are:

Continuous but non-normally distributed
Comparing two independent groups

➡ The appropriate test is a Mann–Whitney U test (non-parametric alternative to independent t-test).

🔹 Hypothetical Data

CBT group PHQ-9 scores:
4, 6, 5, 3, 8, 7, 6, 5, 4, 3, 9, 6

Supportive therapy scores:
8, 10, 7, 9, 11, 12, 6, 8, 10, 9, 13, 7

🔹 Clinical Question

> Is there a statistically significant difference in depression severity between CBT and supportive therapy groups?

🔹 Why Not a t-test?

A t-test assumes:

Normal distribution
Equal variances

Here:

Small sample
Skewed distribution

So we use Mann–Whitney U, which:

Compares ranks rather than means
Tests whether one group tends to have higher values than the other

🔹 Interpretation (Hypothetical Result)

If analysis shows:

U = 20
p = 0.01

Interpretation:

> There is a statistically significant difference in PHQ-9 scores between the CBT and supportive therapy groups. Patients receiving CBT had significantly lower depression scores at 12 weeks.

🔹 How You’d Phrase It in a Paper

> A Mann–Whitney U test showed that PHQ-9 scores were significantly lower in the CBT group (median = 5.5) compared with the supportive therapy group (median = 9.0), U = 20, p = 0.01.

🔹 High-Yield Exam Pearl

Use Mann–Whitney U when:

Comparing 2 independent groups
Data are ordinal OR continuous but non-normal
Sample size is small

🔹 Quick Comparison Memory Hook

Independent t-test → Means → Normal
Mann–Whitney U → Medians → Skewed
Wilcoxon signed-rank → Paired data
Kruskal–Wallis → 3+ independent groups

Question 3

Q

What is a one sample t-test?

Answer

A

For parametric data.

One-Sample t-Test and Paired t-Test

(They are related but answer different questions.)

=====

🔹 1️⃣ One-Sample t-Test

✅ What It Is

A one-sample t-test compares:

> The mean of ONE sample
to
A known or hypothesised population mean

It answers:

> “Is my sample different from a known value?”

It assumes:

Continuous data
Approximately normal distribution
Independent observations

====

🩺 Clinical Example 1 – Lithium Level Monitoring

Therapeutic lithium level is 0.6 mmol/L.

A registrar measures lithium levels in 15 patients at 6-month review.

Mean lithium level in the clinic sample = 0.72 mmol/L

Clinical question:

> Is our clinic’s mean lithium level significantly different from the recommended therapeutic target (0.6 mmol/L)?

A one-sample t-test compares:

Sample mean = 0.72
Population mean = 0.6

If p < 0.05 → clinic prescribing pattern significantly differs from target.

====

🩺 Clinical Example 2 – Length of Stay Audit

National average psychiatric inpatient stay = 21 days.

Your ward’s last 20 discharges:
Mean LOS = 25 days.

Question:

> Is our ward’s mean length of stay significantly different from the national average?

→ Use a one-sample t-test.

====

🔑 Exam Memory Hook

One sample → one group vs one known number

====

Question 4

Q

What is the non-parametric version of a one-sample (paired) T test?

Answer

A

Wilcoxon matched pairs test.

💍 2️⃣ Wilcoxon Matched Pairs = Non-Parametric Paired t-test
💒 Memory Hook:
“The Wedding Without the Bell Curve.”

A wedding = pairs 👰🤵

The paired t-test is the classy wedding that requires a perfect bell-shaped cake 🎂 (normal distribution).

The Wilcoxon wedding?
Still paired…
But the cake collapsed.
No bell curve required.

Logical link:

Same people measured twice

Paired t-test → compares mean difference

Wilcoxon → ranks the differences

Same structure, just no normality assumption

🔑 Trigger phrase:

“Same people twice? If the bell curve dies — invite Wilcoxon.”

Question 5

Q

What is the difference between an unapired t-test and paired t-test?

Answer

A

Great question — this is high-yield stats and examiners love it.

🧠 Core Difference in One Line

Unpaired (Independent) t-test → compares two different groups
Paired t-test → compares the same group measured twice (or matched pairs)

1️⃣ Unpaired (Independent) t-test

📌 What it compares

Two separate, unrelated groups

📌 Research question

> “Are the means of these two independent groups different?”

📌 Clinical examples

Mean depression score in CBT group vs SSRI group
Mean systolic BP in smokers vs non-smokers
Mean BMI in men vs women

📌 Key assumption

The two groups are independent (no overlap, no pairing)

🧠 Memory Hook

Think:
👬 UNpaired = UNrelated groups

Two strangers in a bar. No relationship.

2️⃣ Paired t-test (Dependent t-test)

📌 What it compares

Two measurements from the same participants

📌 Research question

> “Did the mean change within this group?”

📌 Clinical examples

Depression score before and after CBT
Weight before and after diet program
Blood glucose before and after insulin

Each person acts as their own control.

🧠 Memory Hook

👫 Paired = Partners

Same person, two time points.
Like checking your weight before and after Christmas 🎄🍰

🔬 Why This Matters Statistically

🔥 Clinical Pearl

Paired t-tests are more powerful because they remove individual baseline differences.

Example:
If someone naturally has high anxiety, that baseline trait doesn’t distort the result — you only measure their change.

🚨 Common Exam Trap

If the same participants are measured twice and you choose unpaired → ❌ Wrong.

If two separate groups and you choose paired → ❌ Wrong.

Always ask:

> Are these the same people?

⚡ Ultra-Short Summary

Unpaired = Between groups
Paired = Within subjects
Paired controls for individual differences
Both assume normally distributed data

Question 6

Q

What is a paired t-test?

Answer

A

🔹 2️⃣ Paired t-Test (Dependent t-Test) - PAIRED T-TEST/ DEPENDENT T-TEST

✅ What It Is

A paired t-test compares:

> Two measurements taken from the SAME individuals

It answers:

> “Did this group change?”

It assumes:

Continuous data
Differences are approximately normally distributed
Measurements are dependent (paired)

====

🩺 Clinical Example 1 – Antidepressant Trial

PHQ-9 scores measured:

Before SSRI
After 8 weeks of SSRI

Each patient has:

Pre-treatment score
Post-treatment score

We compare:

> Mean difference in PHQ-9 within the same patients.

This is NOT independent groups — it’s the same people.

So we use a paired t-test.

====

🩺 Clinical Example 2 – Clozapine and Weight Gain

Patients weighed:

At baseline
At 6 months on clozapine

Question:

> Has weight significantly increased?

→ Paired t-test compares weight before and after in the same individuals.

====

🔬 Why Not Independent t-Test?

Because measurements are not independent.

Using an independent t-test would:

Ignore within-person pairing
Reduce statistical power
Be incorrect

====

🔹 The Key Concept Difference
(See attached)

====

🔑 Ultra-High-Yield Summary

One sample = one group vs fixed number
Paired = before vs after (same people)
Independent = group A vs group B

====
🧠 Exam Trap Alert

If you see:

“Before and after” → paired
“Two groups” → independent
“Compared to national average” → one-sample

Question 7

Q

What is a Wilcoxon matched pairs test?

Answer

A

📊 Wilcoxon Matched-Pairs Test (Wilcoxon Signed-Rank Test)

🧠 What Is It?

The Wilcoxon matched-pairs test (also called the Wilcoxon signed-rank test) is the non-parametric alternative to the paired t-test.

👉 It compares two related measurements from the same participants, but
👉 it does NOT assume normal distribution.

Instead of comparing means, it compares the ranks of the differences.

🩺 Clinical Examples

1️⃣ Depression scores before & after therapy

HAM-D score before CBT
HAM-D score after CBT
Data are skewed (common in clinical samples)
→ Use Wilcoxon

2️⃣ Pain scores pre- and post-surgery

Pain scales (0–10) are ordinal, not truly continuous
→ Wilcoxon is more appropriate

3️⃣ CRP levels before and after antibiotics

CRP is often highly skewed
→ Non-normal → Wilcoxon

🔬 What It Actually Tests

It looks at:

The difference between each pair
Ranks the absolute differences
Applies signs (+/–)
Tests whether positive and negative ranks balance out

If most differences go in one direction → statistically significant.

🧪 Exam-Ready Comparison: Wilcoxon vs Paired t-test
(See comparison table)

🎯 High-Yield Exam Logic

If question says:

“Same participants measured twice” → think paired test
“Data are skewed” or “not normally distributed” → think Wilcoxon
“Ordinal scale (Likert, pain scale)” → think Wilcoxon

If it says:

“Normally distributed differences” → choose paired t-test

⚡ Quick Decision Algorithm

Same people twice?

→ YES
Are data normally distributed?
→ YES → Paired t-test
→ NO → Wilcoxon

→ NO
Use independent tests instead

🧠 Memory Hook

💍 Wilcoxon = “Wickedly non-normal wedding”

Wedding = paired
Wicked = weird distribution
No normality allowed 🎭

🔥 Clinical Pearl

Most real-world psychiatric scales (e.g. Likert-based symptom ratings) are technically ordinal and often skewed — which makes Wilcoxon statistically more correct, even though many studies still use paired t-tests for convenience.

🧾 Ultra-Short Summary (Exam Version)

The Wilcoxon matched-pairs test is the non-parametric alternative to the paired t-test used for two related samples when data are ordinal or not normally distributed. It compares ranked differences rather than mean differences.

–

Love this 😄 — let’s make it 10-year-old simple.

🎒 The Sticker Test Example

Imagine you have 6 kids.

You give them a new “Super Study Juice” 🧃 and test how many spelling words they get right:

Once before the juice
Once after the juice

Because it’s the same kids twice, this is a paired situation.

📊 The Scores

🤔 What Are We Trying to See?

Did the juice actually help?

But here’s the twist:

Maybe the scores are kind of messy and not nicely spread out.
So instead of looking at averages, we do something simpler.

🏅 What Wilcoxon Does (Kid Version)

Instead of asking:

> “What’s the average improvement?”

It asks:

> “Did most kids get better?”

Step 1️⃣

Look at how much each kid improved.

Amy: +3
Ben: +1
Cara: +5
Dan: 0
Eva: +3
Finn: +1

Step 2️⃣

Rank the improvements (smallest to biggest)

We don’t care about exact numbers — just who improved a little vs a lot.

Step 3️⃣

Check direction

If most improvements are positive, the juice probably helped.

If half went up and half went down → probably no effect.

🧠 The Big Idea

Wilcoxon is like saying:

👉 “I don’t care about fancy averages.
👉 I just want to know if most people improved.”

🆚 Compared to Paired t-test (Kid Version)

🧁 Even Simpler Analogy

Paired t-test =
📏 “Let’s measure exactly how much taller everyone grew.”

Wilcoxon =
🏆 “Let’s line them up and see who grew more than who.”

💡 One-Sentence Memory Trick

Wilcoxon = “Were most kids better?”
Paired t-test = “How much better on average?”

Kid | Before | After |
| —- | —— | —– |
| Amy | 5 | 8 |
| Ben | 6 | 7 |
| Cara | 4 | 9 |
| Dan | 7 | 7 |
| Eva | 3 | 6 |
| Finn | 8 | 9 |

Question 8

Q

What is a one way analysis of variance F test using total sum of squares? (One-way ANOVA)

Answer

A

📊 One-Way Analysis of Variance (ANOVA) — The F Test

(using Total Sum of Squares)

🧠 What Is It? (Exam-Ready)

A one-way ANOVA tests whether the means of 3 or more independent groups are different.

It uses an F-test, which compares:

> 🔹 Variability between groups
to
🔹 Variability within groups

If between-group variation is much bigger than within-group variation → the means are likely different.

🧮 The Key Idea: Total Sum of Squares (SST)

Think of total variability in your data as a pie 🥧

Total variation = SST (Total Sum of Squares)

This gets split into two parts:

1️⃣ Between-group variation (SSB)
→ How far group means are from the overall mean

2️⃣ Within-group variation (SSW)
→ How spread out people are inside each group

The Formula Logic
(See attached image of formula)

If groups are truly different → SSB will be large → F will be large.

🩺 Clinical Examples

1️⃣ Comparing 3 antidepressants

You measure depression scores in patients on:

Sertraline
Venlafaxine
Mirtazapine

Question:

> Is at least one drug’s mean score different?

Use one-way ANOVA.

2️⃣ Comparing therapy types

You compare:

CBT
Psychodynamic therapy
Supportive therapy

Measure mean anxiety reduction.

Again → one-way ANOVA.

🔥 Exam Pearl

If you compare more than two independent groups, use ANOVA, not multiple t-tests.

Multiple t-tests inflate Type I error.

👶 Explanation for a 10-Year-Old

🍦 Ice Cream School Example

Three classes eat different ice creams:

Chocolate
Vanilla
Strawberry

Afterward, you measure how happy each class is.

Now you ask:

> Are the classes happy because of the flavour,
or are kids just randomly different in happiness?

Step 1: Look at Total Mess (Total Variation)

All kids have different happiness levels.
That’s your total mess (Total Sum of Squares).

Step 2: Split the Mess

Some mess happens because:

Different flavours might make classes happier (Between-group variation)

Some mess happens because:

Kids are just different from each other (Within-group variation)

Step 3: Compare Them

If:

Classes are very different from each other
AND
Kids inside each class are pretty similar

Then flavour probably matters.

That comparison = the F test

🧠 What Does the F Mean?

F is basically asking:

> “Is the difference between groups bigger than the random noise inside groups?”

If YES → big F → significant result.

📊 Clean Exam Comparison

🧠 Memory Hook

ANOVA = “Another Number Of Various Averages”

Or better:

> ANOVA asks:
“Are the groups different, or is it just noise?”

And remember:

⚡ Ultra-Short Summary (Exam Version)

One-way ANOVA tests whether three or more independent group means differ by partitioning total variance into between-group and within-group components. The F statistic compares these two sources of variance.

Question 9

Q

What is the non-parametric alternative to a one-way ANOVA?

Answer

A

A Kruskall-Wallis test.

🥊 1️⃣ Kruskal–Wallis = Non-Parametric One-Way ANOVA
🎤 Memory Hook:
“ANOVA Brings Averages. Kruskal Brings a Ranking Contest.”

Imagine:

👔 ANOVA walks into a conference room with a calculator saying:

“Let’s compare the averages of these 3 groups.”

Then 🎖️ Kruskal–Wallis bursts in and says:

“Forget averages. Line them ALL up. I’m ranking everybody.”

Why this works logically:

One-way ANOVA → compares means across 3+ independent groups

Kruskal–Wallis → compares ranks across 3+ independent groups

Same structure (3+ independent groups)

Just swaps means → ranks

🔑 Trigger phrase:

“Three groups? If messy data — rank the crowd.”

Question 10

Q

What’s the non-parametric equivalent of an unpaired T-test?

Answer

A

Mann-Whitney U test - non-parametric unpaired t-test.

🥊 3️⃣ Mann–Whitney U = Non-Parametric Unpaired t-test
⚔️ Memory Hook:
“Two Teams, No Averages — Just a Tug-of-War.”

Picture two teams pulling a rope.

👨‍🔬 Unpaired t-test says:

“Let’s compare the average strength of each team.”

🏋️ Mann–Whitney says:

“Nope. Let’s mix everyone together, rank them, and see which team keeps winning the top spots.”

Logical link:

Two independent groups

Unpaired t-test → compares means

Mann–Whitney → compares ranks

Same setup, just no normality required

🔑 Trigger phrase:

“Two separate teams? If data are ugly — rank the fight.”

Question 11

Q

Compare PURPOSE/STUDY GROUP of each test, provide its non-parametric twin, and provide a clinical example.

1) Paired t-test
2) Unpaired t-test
3) One-way ANOVA
4) Two-way ANOVA

Answer

A

See attached image.

Question 12

Q

What is a two-way analysis of variance? (Two way ANOVA)

Answer

A

🧠 What Is Two-Way ANOVA?

Two-way ANOVA tests:

1️⃣ The effect of Factor A
2️⃣ The effect of Factor B
3️⃣ The interaction between them

🩺** Clinical Example Explained**
Suppose you study:

Therapy type: CBT vs Psychodynamic
Sex: Male vs Female

You’re asking:
1) Does therapy type matter?
2) Does sex matter?
3) Does therapy work differently depending on sex? (interaction)

That last question is the big one.

🎯 Why There’s No Simple Non-Parametric Twin

For:
2 groups → Mann–Whitney
3+ groups → Kruskal–Wallis

But for two independent variables, things get more complicated.
There is no clean, exam-friendly non-parametric twin like the others.
Advanced options exist (e.g., aligned rank transform), but they’re rarely tested clinically.

Question 13

Q

What is a chi squared test?

Answer

A

Perfect — let’s make this clear, simple, exam-ready, and include the null hypothesis properly.

AssoCHIation between discrete variables

📊 Chi-Squared (χ²) Test — Distribution-Free Test

🧠 What Is It?

A chi-squared (χ²) test is a non-parametric (distribution-free) test used to compare categorical (discontinuous) variables between two or more independent groups.

It tests whether:

> The distribution of a categorical variable is the same across groups.

🎯 The Null Hypothesis (This Is High-Yield)

The null hypothesis (H₀) says:

> There is no association between the variables.
The distribution of the categorical variable is the same in all groups.

In simpler words:

> Any differences in proportions happened by chance.

🔬 Even Simpler Version (Cleaned-Up Statement)

A chi-squared test examines whether the distribution of a categorical (discontinuous) variable is the same across two or more independent samples.
It is called “distribution-free” because it does not assume normality.

🧮 What Does It Actually Compare?

It compares:

Observed frequencies (what you actually see)
Expected frequencies (what you would expect if there were no relationship)

If observed ≠ expected by a lot → χ² is large → reject H₀.

🩺 Clinical Examples

1️⃣ Smoking & Schizophrenia

Question:

> Is smoking status associated with schizophrenia?

Variables:

Smoking (yes/no)
Schizophrenia (yes/no)

Null hypothesis:

> Smoking rates are the same in people with and without schizophrenia.

2️⃣ Drug Response (Responder vs Non-responder)

Question:

> Is response rate different between SSRI and SNRI?

Null hypothesis:

> Proportion of responders is the same for both drugs.

3️⃣ Side Effects by Sex

Question:

> Is weight gain associated with sex?

Null hypothesis:

> The proportion with weight gain is the same in males and females.

👶 10-Year-Old Explanation

Imagine two classrooms choose snacks:

You think boys and girls choose snacks equally.

The null hypothesis says:

> “There is no real difference. Any weird pattern happened by chance.”

You compare:

What you expected if everyone chose randomly
What actually happened

If they’re very different → probably not random.

That’s chi-squared.

🧠 When Do You Use It?

Use χ² when:

Data are categorical
You are comparing proportions
Groups are independent
Sample size is adequate

⚠️ Exam Pearl

If expected cell counts are very small (<5) → use Fisher’s Exact Test instead.

🧠 Memory Hook

χ² = “Compare the Counts”

If you’re counting people in boxes (Yes/No, Male/Female, Drug A/Drug B) → think chi-squared.

⚡ Ultra-Short Exam Summary

The chi-squared test is a non-parametric, distribution-free test that assesses whether the distribution of a categorical variable differs across two or more independent groups by comparing observed and expected frequencies.

Yes, but why is it called a Chi-Squared Test?
I love this question 😄

Let’s explain it like you’re 10.

🎲 Why Is It Called “Chi-Squared”?

First:

Chi (χ) is just a Greek letter.
It’s pronounced “kai” (like “sky”).

So “chi-squared” just means:

> “The chi number, squared.”

🧮 What Gets Squared?

When we do a chi-squared test, we:

1️⃣ Look at what we expected to happen
2️⃣ Look at what we actually saw
3️⃣ Find the difference

Then we:

👉 Square the difference

Why square it?

Because:

It makes all differences positive (no cancelling out)
Bigger mistakes become MUCH bigger

So if something is way off from expected, squaring makes it stand out.

🧁 10-Year-Old Example

Imagine you think:

> Half the class likes chocolate.
Half likes vanilla.

You expect:

10 chocolate
10 vanilla

But you actually see:

16 chocolate
4 vanilla

That’s a big difference!

You calculate:

Observed − Expected
Then square it

Big difference → big squared number → big chi-squared value.

🎯 Why the “Chi” Part?

When mathematicians worked out the math for these squared differences,
they discovered the final number follows a special curved shape.

They named that curve:

The chi-squared distribution

So the test is called:

> The test that uses the chi-squared distribution.

🧠 Super Simple Summary

It’s called chi-squared because:

We calculate differences
We square them
The final number follows something called the chi-squared distribution

🧠 Even Simpler Version

Chi-squared =

> “How big are the squared surprises?”

Big surprises → big chi-squared → something interesting is happening.

Question 14

Q

Compare a chi squared test and a Fisher’s exact test?

Answer

A

Great question — this is a classic exam comparison 🔥

Both tests examine associations between categorical variables, but they differ in how they calculate probability and when they should be used.

📊 What Do They Have in Common?

Both:

Compare categorical data
Test the null hypothesis that there is no association between variables
Are used with independent groups
Often applied to 2×2 tables

Example structure:

🧠 The Big Difference
(See comparison table)

🎯 When Do You Use Each?

✅ Use Chi-Squared when:

Sample size is large
Expected cell counts are ≥ 5
You’re happy using a probability approximation

✅ Use Fisher’s Exact Test when:

Sample size is small
Any expected cell count < 5
You want an exact p-value

🩺 Clinical Examples

1️⃣ Large Sample Example (Chi-Squared)

Study of 500 patients:

Is smoking associated with schizophrenia?

| | Schizophrenia | No Schizophrenia |
| ———- | ————- | —————- |
| Smoker | 120 | 180 |
| Non-smoker | 80 | 120 |

All cell counts are large → use chi-squared.

2️⃣ Small Sample Example (Fisher’s Exact)

Rare adverse event in a small RCT (n=20):

| | Seizure | No Seizure |
| ——- | ——- | ———- |
| Drug | 3 | 7 |
| Placebo | 0 | 10 |

One cell has 0 and expected counts are small → use Fisher’s exact test.

👶 10-Year-Old Explanation

Imagine you’re checking if boys and girls prefer chocolate.

If you ask 200 kids:

You can estimate the answer pretty well → chi-squared is fine.

But if you only ask 8 kids:

Your estimate might be shaky.
So Fisher’s test counts all possible ways the results could happen and calculates the exact chance.

Chi-squared = good estimate
Fisher = exact calculation

🧠 Why Is Fisher “Exact”?

Chi-squared uses a shortcut based on a curve.

Fisher:

Calculates the exact probability of getting your table (or something more extreme)
No approximation needed

That’s why it’s better for small numbers.

🔥 Exam Pearl

If the stem says:

> “Small sample size”
“Rare event”
“Expected cell count less than 5”

Choose Fisher’s exact test.

🧠 Memory Hook

Chi-squared = “Big crowd? Estimate is fine.”
Fisher = “Tiny crowd? Count every possibility.”

⚡ Ultra-Short Exam Summary

Chi-squared is an approximate test of association for categorical variables used in larger samples, while Fisher’s exact test calculates the exact probability of association and is preferred when expected cell counts are small.

| Outcome Yes | Outcome No |
| ———– | ———– | ———- |
| Exposed | | |
| Not Exposed | | |

Question 15

Q

What is a Fisher’s exact test?

Answer

A

🧪 Fisher’s Exact Test

🧠 What Is It?

Fisher’s exact test is a statistical test used to examine whether there is an association between two categorical variables, usually in a 2×2 table, when the sample size is small.

It tests the null hypothesis that:

> There is no association between the two variables
(i.e., the proportions are the same in both groups).

It is called “exact” because it calculates the exact probability of observing the data (or something more extreme), rather than using an approximation like the chi-squared test.

🎯 The Null Hypothesis (Very High-Yield)

The null hypothesis (H₀) states:

There is no association between the two categorical variables.
The proportions are the same in both groups.

In simple terms:

Any difference in proportions happened purely by chance.

Fisher’s exact test calculates the exact probability of observing the data (or something more extreme) assuming the null hypothesis is true.

If that probability (p-value) is very small → we reject the null hypothesis.

📊 When Do You Use It?

Use Fisher’s exact test when:

Data are categorical
Groups are independent
Sample size is small
Any expected cell count is less than 5

🩺 Clinical Examples

1️⃣ Rare Adverse Event in a Small Trial

A small RCT (n=20) studies whether a new antidepressant causes seizures.

Because:

Sample size is small
One cell has 0
Expected counts are low

→ Use Fisher’s exact test.

2️⃣ Rare Genetic Mutation & Disease

You examine whether a rare mutation is associated with a rare neurological disorder.

| | Mutation | No Mutation |
| ———- | ——– | ———– |
| Disease | 2 | 8 |
| No Disease | 1 | 19 |

Small numbers → Fisher’s exact test.

3️⃣ Case-Control Study with Small Sample

Investigating whether cannabis use is associated with psychosis in a small rural sample (n=30).

If some cells have small counts → use Fisher’s exact test.

🔬 How It Differs from Chi-Squared
(See comparison table)

👶 10-Year-Old Explanation

Imagine you flip a coin 200 times.
If something strange happens, you can estimate whether it’s weird.

But if you flip a coin only 4 times:

You can’t really estimate — you have to count all possible ways the flips could happen.

Fisher’s test does that counting.
It checks every possible way the table could look and calculates the exact chance.

🧠 Why It’s Important Clinically

In medicine:

Rare side effects
Rare diseases
Small pilot trials

are common.

Chi-squared can give misleading results with small numbers.
Fisher’s exact test is more accurate in those cases.

⚡ Ultra-Short Exam Summary

Fisher’s exact test is a non-parametric test used to determine whether two categorical variables are associated in small samples by calculating the exact probability of the observed distribution.

🧠** Memory Hook**

🎣 Fisher “catches the exact probability” when the sample is small.

If the crowd is tiny and the counts are small:

Don’t estimate — let Fisher count every fish in the pond.

Small sample
Exact probability
Tests association
Under the null of no difference

| | Seizure | No Seizure |

——- | ——- | ———- |
| Drug | 3 | 7 |
| Placebo | 0 | 10 |

Question 16

Q

What is the product moment correlation coefficient (aka ‘Pearson’s r’)?

Answer

Study These Flashcards

A

(Pearson is like the parametric version of Spearman)
(Spearman is the non-parametric version of Pearson)

📈 Product–Moment Correlation Coefficient (Pearson’s r)

🧠 What Is It?

The product–moment correlation coefficient, better known as Pearson’s r, measures:

> The strength and direction of a linear relationship between two continuous variables.

It ranges from:

+1 → perfect positive linear relationship
0 → no linear relationship
–1 → perfect negative linear relationship

🎯 What Is the Null Hypothesis?

The null hypothesis (H₀) states:

> There is no linear correlation between the two variables in the population
(r = 0).

If the p-value is small → reject H₀ → there is evidence of a linear relationship.

📊 What Does “Product–Moment” Mean?

It sounds scary, but it just means:

We look at how two variables move together
We multiply their deviations from their means
Then standardise the result

You don’t need the formula for most clinical exams — just remember:

> Pearson’s r measures how closely two continuous variables move together in a straight-line pattern.

🩺 Clinical Examples

1️⃣ Depression Severity & Sleep Hours

Do higher HAM-D scores correlate with fewer hours of sleep?

Variable 1: HAM-D score (continuous)
Variable 2: Hours of sleep (continuous)

If worse depression is linked to less sleep → r would be negative.

2️⃣ Lithium Level & Serum Creatinine

Is higher lithium concentration associated with higher creatinine?

Both continuous variables.

If higher lithium correlates with higher creatinine → r positive.

3️⃣ Age & Blood Pressure

Is increasing age associated with higher systolic BP?

Likely a positive correlation.

📊 Interpreting r

⚠️ Important Assumptions (Exam-Relevant)

Pearson’s r assumes:

Both variables are continuous
Relationship is linear
Data are approximately normally distributed
No major outliers

If data are not normal or relationship isn’t linear → use Spearman’s rank correlation instead.

👶 10-Year-Old Explanation

Imagine:

You measure:

How tall kids are
How much they weigh

Usually:

Taller kids weigh more.

If they go up together → positive correlation.

If one goes up and the other goes down → negative correlation.

If there’s no pattern → correlation near zero.

Pearson’s r is just a number that tells you:

> “How strongly do these two things move together in a straight line?”

🧠 Memory Hook

📏 Pearson = “Pair of continuous variables moving together.”

If:

Two continuous numbers
Looking for linear relationship

Think: Pearson’s r

⚡ Ultra-Short Exam Summary

Pearson’s r is a parametric measure of the strength and direction of the linear relationship between two continuous variables, testing the null hypothesis that there is no correlation (r = 0).

NB: CORRELATION DOES NOT MEAN CAUSATION

| r value | Meaning |

——- | —————————- |
| +0.8 | Strong positive relationship |
| +0.4 | Moderate positive |
| 0 | No linear relationship |
| –0.4 | Moderate negative |
| –0.8 | Strong negative |

Question 17

Q

Compare Pearson’s product-moment correlation coefficent and Spearman’s rank correlation coefficient?

Answer

Study These Flashcards

A

Perfect — this is a very exam-favourite comparison 🔥

Let’s make it crystal clear, clinically grounded, and very memorable.

📊 Pearson vs Spearman — Clear Comparison
(see attached table)

🧠 What’s the Real Difference?

Pearson asks:

> “Do these two continuous variables move together in a straight line?”

Spearman asks:

> “If one goes up, does the other generally go up too?”
(Even if not perfectly linear)

🩺 Clinical Examples

🧪 Example 1: Depression Score & Sleep Hours

HAM-D score (continuous)
Hours slept (continuous)

If the relationship looks roughly straight-line → use Pearson.

If the relationship is curved or skewed → use Spearman.

🧪 Example 2: Pain Severity (Likert 1–5) & Disability Score

Pain scale is ordinal.

→ Use Spearman.

🧪 Example 3: Lithium Level & Creatinine

Both continuous and roughly normal → Pearson.

If extreme outliers present → Spearman safer.

🎯 Exam Logic Shortcut

Two continuous variables + normal + linear → Pearson

Ordinal OR skewed OR outliers → Spearman

👶 10-Year-Old Explanation

📏 Pearson

Imagine drawing a straight line through dots on a graph.

Pearson asks:

> “How straight is this line?”

🏆 Spearman

Imagine lining kids up from shortest to tallest.

Then lining them up by weight.

Spearman asks:

> “Do the same kids stay near the top in both lines?”

It doesn’t care about exact numbers — just order.

🧠 Memory Hooks (Very Different + Logical)

📏 Pearson Memory Hook

“Pear-son = Perfectly Straight Person”

Pearson only likes:

Straight lines
Proper continuous data
No weird outliers

If the graph isn’t straight, Pearson gets upset.

Trigger phrase:

> “Straight line? Call Pearson.”

🏆 Spearman Memory Hook

“Spear-man Throws Away the Numbers and Keeps the Ranks”

Imagine a warrior named Spearman 🛡️

He throws away messy numbers
Keeps only the rankings

He doesn’t care if the line curves —
As long as higher ranks go with higher ranks.

Trigger phrase:

> “Messy data? Rank it with Spearman.”

🔥 Key Concept: Linear vs Monotonic

Linear → straight line

Monotonic → always going up or always going down (even if curved)

Pearson needs linear.
Spearman just needs monotonic.

🧠 Ultra-Clean Exam Summary

Pearson’s r is a parametric measure of linear correlation between two continuous variables, while Spearman’s rho is a non-parametric rank-based measure of monotonic association used when data are ordinal, skewed, or non-linear.

This is excellent. We are upgrading the memory palace. 😄

Let’s make this unforgettable.

🍐📏 Pearson vs 🛡️🏹 Spearman — The Ultimate Mental Picture

🎉 Scene 1: Pearson the Pear Pansy

You walk into a garden party.

Standing there is Pearson.

He is:

Wearing a giant pear costume 🍐
Holding a delicate silver ruler 📏
Eating pear tarts and pear sorbet
Complaining about the symmetry of the table setting

He says in a dramatic voice:

> “If it’s not perfectly straight, I refuse to measure it.”

He only likes:

Smooth, straight lines
Proper continuous numbers
No messy outliers

If one datapoint sticks way out?

He faints into a bowl of pear custard.

🍐 What Pearson Stands For

Continuous variables
Linear relationship only
Parametric (assumes normality)
Sensitive to outliers

📏 Pear-son = Pear + Straight ruler

If it’s not straight, he cannot cope.

🛡️🏹 Scene 2: Spearman the Rugged Warrior

Now imagine a mountain path.

Enter Spearman.

He is:

Wearing hiking boots
Carrying a spear
Covered in dirt
Calmly climbing a rugged, winding hill

The path is curved.
It twists.
It’s not straight at all.

Spearman says:

> “Doesn’t matter. Are we generally going uphill? Good enough.”

He lines everyone up by rank.

He doesn’t care about:

Exact distances
Curves
Messy data

Outlier off in the bushes?

He shrugs:

> “Still last in rank.”

🛡️ What Spearman Stands For

Uses ranks
Non-parametric
Works with ordinal or skewed data
Needs monotonic trend (always up or always down)
Robust to outliers

🏹 Spear-man = Rugged, flexible, rank-focused

🧠 Lock It In

Picture this:

🍐 Pearson in a pear costume with a ruler crying because the graph is curved.

🏹 Spearman hiking a mountain saying,
“As long as it goes up overall, we’re fine.”

⚡ Ultra-Fast Recall Rule

Straight, clean, continuous → 🍐 Pearson

Curved, messy, ranked → 🛡️ Spearman

If you’d like, I can now create a similar absurd memory pair for:

ANOVA vs Kruskal
t-test vs Mann–Whitney
Chi-square vs Fisher

We can build an entire statistical Avengers team 😄

Question 18

Q

What is regression by the least squares method?

Answer

Study These Flashcards

A

📈 Regression by the Least Squares Method

🧠 What Is It?

Regression by the least squares method is a statistical technique used to find the best-fitting straight line that predicts one continuous variable from another.

It is most commonly called:

> Simple linear regression

The “least squares” part means:

> We choose the line that makes the sum of the squared errors as small as possible.

📏 What Does That Mean?

Imagine plotting points on a graph.

Some dots are above the line.
Some are below.

Each dot has an error (distance from the line).

We:

1️⃣ Measure each vertical distance
2️⃣ Square it (so negatives don’t cancel positives)
3️⃣ Add them all up

The best line is the one with the smallest total squared error.

That’s why it’s called least squares.

🧪 Is It Parametric?

✅ Yes — linear regression is considered a parametric method.

Why?

Because it assumes:

Linear relationship
Normally distributed residuals (errors)
Homoscedasticity (equal variance of errors)
Independence of observations

It estimates parameters:

Intercept (β₀)
Slope (β₁)

That’s what makes it parametric.

📊 What Does It Actually Do?

Regression answers:

> “How much does Y change when X changes?”

Equation:

[
Y = \beta_0 + \beta_1 X
]

β₀ = intercept
β₁ = slope

🩺 Clinical Examples

1️⃣ Age Predicting Blood Pressure

Question:

> How much does systolic BP increase per year of age?

Age = predictor (X)
Blood pressure = outcome (Y)

Regression estimates the slope.

2️⃣ Lithium Level Predicting Creatinine

Question:

> Does higher lithium level predict higher creatinine?

Lithium = X
Creatinine = Y

Regression tells you how much creatinine increases per unit lithium.

3️⃣ Depression Severity Predicting Functioning

HAM-D score predicting work functioning score.

Regression gives a predictive relationship.

🔥 Correlation vs Regression

Correlation (Pearson’s r):

Measures strength of association
Symmetrical (X and Y interchangeable)

Regression:

Predicts Y from X
Directional

👶 10-Year-Old Explanation

Imagine you’re throwing darts at a board 🎯

Each dart lands somewhere.

Now you draw a straight line that goes through the middle of all the darts.

Some darts are above.
Some are below.

You measure how far each dart is from the line.

Then you:

Square the distances
Add them up

You move the line until those squared distances are as small as possible.

That’s the “least squares” line.

🧠 Even Simpler

It’s just:

> “The straight line that misses the points by the smallest amount overall.”

🎯 What Does the Null Hypothesis Say?

The null hypothesis:

> The slope (β₁) = 0
There is no relationship between X and Y.

If slope ≠ 0 significantly → evidence of association.

🧠 Memory Hook

📏 Least Squares = “Smallest Total Squared Mistakes”

Regression = “Predicting with the best straight line.”

If you’re drawing a line through data and minimizing squared errors → think regression.

⚡ Ultra-Short Exam Summary

Regression by the least squares method is a parametric technique that fits the best linear prediction line between a continuous predictor and outcome by minimizing the sum of squared residuals, testing the null hypothesis that the slope equals zero.

Question 19

Q

Compare regression vs. correlation.

Answer

Study These Flashcards

A

Excellent — this is a high-yield conceptual distinction 🔥

Many people confuse these, but they answer different questions.

📊 Correlation vs Regression — Clear Comparison

🧠 Core Difference in One Line

Correlation asks:
👉 “How strongly are these two variables related?”
Regression asks:
👉 “How much does Y change when X changes?”

🩺 Clinical Examples

1️⃣ Depression & Sleep

You measure:

HAM-D score
Hours of sleep

Correlation:

> Are worse depression scores associated with fewer hours of sleep?

You get r = –0.6 → strong negative relationship.

Regression:

> For every 1-point increase in HAM-D, how many fewer hours of sleep do we expect?

You get:
[
Sleep = 8 - 0.2(HAM\text{-}D)
]

That gives you a predictive formula.

2️⃣ Lithium & Creatinine

Correlation:

Are higher lithium levels associated with higher creatinine?

Regression:

How much does creatinine increase per mmol/L increase in lithium?

Regression gives you a clinically meaningful slope.

🔬 Conceptual Difference

Correlation:

Describes relationship
Symmetrical
No causation implied
No prediction equation

Regression:

Directional
Predicts outcome
Estimates effect size (slope)
Still doesn’t prove causation (but often used in causal models)

👶 10-Year-Old Explanation

Imagine height and weight.

Correlation says:

> “Do tall kids usually weigh more?”

Regression says:

> “If a kid grows 10 cm taller, how much heavier will they probably be?”

Correlation = Are they related?
Regression = How much change happens?

🧠 Memory Hook

💞 Correlation = “Are they dancing together?”
📏 Regression = “How much does one pull the other?”

Or even simpler:

Correlation = friendship
Regression = prediction

⚡ Ultra-Short Exam Summary

Correlation measures the strength and direction of association between two variables, whereas regression estimates the magnitude of change in an outcome variable per unit change in a predictor variable and provides a predictive equation.

Question 20

Q

What is non-parametric regression?

Answer

Study These Flashcards

A

Great — now we’re stepping into slightly more advanced territory 👌

Let’s make it clear, structured, and clinically grounded.

📈 What Is Non-Parametric Regression?

🧠 Simple Definition

Non-parametric regression is a way of modelling the relationship between variables without assuming a specific functional form (like a straight line) and without strict distributional assumptions (e.g., normality).

Unlike linear regression, it does not assume:

A linear relationship
Normally distributed residuals
A specific equation form

Instead, it lets the data “speak for themselves.”

🔬 How Is It Different from Linear Regression?

So:

Linear regression = “Fit the best straight line.”
Non-parametric regression = “Fit the best curve without assuming its shape.”

🩺 Clinical Example 1: Age & Cognitive Decline

Suppose cognitive score declines:

Slowly in midlife
Rapidly after 75
Then plateaus

That relationship is curved, not straight.

A linear regression would misrepresent it.

Non-parametric regression can model the curve naturally.

🩺 Clinical Example 2: Drug Dose & Side Effects

At low doses:

Minimal side effects

Mid doses:

Sharp increase

High doses:

Plateau

This is not linear.

Non-parametric regression can model that shape without forcing a straight line.

🩺 Clinical Example 3: Stress & Performance

The relationship might be:

Low stress → poor performance
Moderate stress → peak performance
High stress → poor performance

That’s an inverted U-shape.

Linear regression cannot capture that well.
Non-parametric regression can.

📊 Common Non-Parametric Regression Methods

These are not always tested at basic clinical level, but good to know:

1️⃣ LOESS (Locally Weighted Scatterplot Smoothing)

Fits small local regressions across data
Produces smooth curve
Very common in epidemiology

2️⃣ Kernel Regression

Uses weighted averages of nearby points
Smooths curve

3️⃣ Spline Regression (when flexible knots used)

Piecewise smooth curves

4️⃣ Rank-Based Regression (less common clinically)

⚠️ Important Clarification

Do not confuse:

Non-parametric correlation (Spearman)
Non-parametric group comparisons (Mann–Whitney, Kruskal–Wallis)

With:

Non-parametric regression

They answer different questions.

Regression = prediction/modelling
Correlation = association strength
Group tests = compare distributions

👶 10-Year-Old Explanation

Imagine you’re drawing a road through a bunch of dots.

Linear regression says:

> “The road must be straight.”

Non-parametric regression says:

> “The road can curve and bend however it needs to follow the dots.”

It doesn’t assume the road’s shape ahead of time.

🧠 When Would You Use It?

Use non-parametric regression when:

The relationship looks curved
Data violate linear assumptions
You don’t want to impose a specific equation
Large sample size is available

🎯 Exam-Ready Summary

Non-parametric regression refers to flexible modelling methods that estimate relationships between variables without assuming a specific parametric form (e.g., linearity or normal residuals), allowing the data to determine the shape of the association.

🧠 Memory Hook

Linear regression = “Ruler.” 📏
Non-parametric regression = “Flexible garden hose.” 🪴

If the data bend, the hose bends with them.

Feature | Linear Regression | Non-Parametric Regression |
| ———————- | —————– | ————————- |
| Assumes straight line? | ✅ Yes | ❌ No |
| Assumes normal errors? | ✅ Yes | ❌ Not required |
| Fits fixed equation? | Y = β₀ + β₁X | Flexible curve |
| Parametric? | Yes | No |

Question 21

Q

What is the difference between simple and multiple regression?

Answer

Study These Flashcards

A

Great question — this is foundational and very testable 🔥

Let’s make it clean, structured, and intuitive.

📊 Simple vs Multiple Regression

🧠 Core Difference in One Line

Simple regression → 1 predictor (independent variable)
Multiple regression → 2 or more predictors

Both usually refer to linear regression unless otherwise specified.

📈 1️⃣ Simple Linear Regression

Structure

[
Y = \beta_0 + \beta_1 X
]

One predictor (X)
One outcome (Y)

What It Asks

> “How much does Y change when X changes?”

🩺 Clinical Example

Does age predict systolic blood pressure?

X = Age
Y = BP

You estimate how much BP increases per year of age.

📈 2️⃣ Multiple Linear Regression

Structure

[
Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3
]

Several predictors
One outcome

What It Asks

> “How much does each predictor affect Y, while holding the others constant?”

This is the key difference.

🩺 Clinical Example

Predicting depression severity using:

Age
Sex
Trauma history
Sleep duration

Multiple regression lets you estimate:

Effect of trauma history
independent of age and sleep

This helps control for confounding.

🔬 Why Multiple Regression Is Powerful

It allows:

Adjustment for confounders
Independent effect estimation
Better prediction
More realistic modelling

Most clinical research uses multiple regression.

🎯 Key Concept: “Holding Other Variables Constant”

Simple regression cannot separate overlapping effects.

Multiple regression can answer:

> “Is smoking still associated with lung cancer after adjusting for age?”

👶 10-Year-Old Explanation

Simple Regression

You ask:

> “Does studying more increase test scores?”

One cause. One result.

Multiple Regression

Now you ask:

> “Do studying, sleep, and eating breakfast affect test scores?”

Now you check each one separately
while keeping the others the same.

🧠 Clean Comparison Table

🧠 Memory Hook

Simple regression = “One arrow.” ➡️

Multiple regression = “Control panel with many knobs.” 🎛️

You adjust one knob at a time to see its independent effect.

⚡ Ultra-Short Exam Summary

Simple regression examines the relationship between one predictor and one outcome, whereas multiple regression estimates the independent effects of two or more predictors on a single outcome while controlling for other variables.

Question 22

Q

What is multiple regression by least squares method?

Answer

Study These Flashcards

A

Excellent — now we’re combining concepts properly 🔥

You already know:

Least squares = best fitting line
Multiple regression = multiple predictors

Now let’s put them together clearly.

📈 Multiple Regression by the Least Squares Method

🧠 What Is It?

Multiple regression by the least squares method is a parametric statistical technique that:

> Models the relationship between one continuous outcome variable and two or more predictor variables
by choosing the regression equation that minimizes the sum of squared residuals (errors).

📐 The Equation

[
Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \dots
]

Where:

Y = outcome (dependent variable)
X₁, X₂, X₃ = predictors
β₀ = intercept
β₁, β₂, β₃ = slopes (independent effects)

The least squares method finds the β values that make the total squared error as small as possible.

🎯 What Does It Test?

For each predictor:

Null hypothesis:

[
\beta_i = 0
]

Meaning:

> That predictor has no independent effect on the outcome.

If β ≠ 0 significantly → independent association exists.

🔬 Why “Least Squares”?

For every observation:

1️⃣ Calculate predicted Y
2️⃣ Calculate error (Observed − Predicted)
3️⃣ Square it
4️⃣ Add all squared errors

The best model = smallest total squared error.

🧪 Is It Parametric?

✅ Yes.

It assumes:

Linear relationship
Normally distributed residuals
Homoscedasticity
Independence
No perfect multicollinearity

🩺 Clinical Examples

1️⃣ Predicting Blood Pressure

Outcome: Systolic BP

Predictors:

Age
BMI
Smoking status

Question:

> How much does BP increase with age, controlling for BMI and smoking?

Each β tells you the independent contribution.

2️⃣ Predicting Depression Severity

Outcome:

HAM-D score

Predictors:

Trauma history
Sleep duration
Substance use
Age

You can estimate the independent effect of trauma while controlling for sleep and substance use.

3️⃣ Predicting Length of Hospital Stay

Outcome:

Days admitted

Predictors:

Diagnosis
Comorbidities
Medication adherence
Social support

This models multiple contributing factors at once.

🧠 Why It’s Important Clinically

Multiple regression:

Adjusts for confounders
Estimates independent effects
Improves prediction
Reflects real-world complexity

Most modern medical research uses this.

👶 10-Year-Old Explanation

Imagine you’re trying to guess how tall someone will be.

You look at:

Their age
Their parents’ height
How much they eat

Instead of using just one thing,
you use all three at the same time.

You draw a “best fit” rule that makes your mistakes as small as possible.

That’s multiple regression using least squares.

🧠 Simple Mental Picture

Simple regression = one lever controlling a machine

Multiple regression = many levers controlling one machine

Least squares = adjust the levers until total mistake is smallest

⚡ Ultra-Short Exam Summary

Multiple regression by the least squares method is a parametric technique that estimates the independent effects of two or more predictors on a continuous outcome by minimizing the sum of squared residuals, testing whether each regression coefficient differs from zero.

Question 23

Q

What is non-parametric multiple regression ? What tests test these? (Advanced)

Answer

Study These Flashcards

A

Excellent — this is more advanced, so I’ll make it clear and structured 👌

📈 What Is Non-Parametric Multiple Regression?

🧠 Simple Definition

Non-parametric multiple regression models the relationship between:

One outcome variable
Two or more predictor variables

Without assuming:

A linear relationship
Normally distributed errors
A specific equation form

Instead of fitting a straight plane (like linear regression does), it allows the relationship to be flexible and data-driven.

🔬 How It Differs from Parametric Multiple Regression

Parametric = “Fit the best flat surface.”
Non-parametric = “Let the surface bend naturally.”

📊 Common Non-Parametric Multiple Regression Methods

These are modelling techniques rather than single “tests.”

1️⃣ LOESS / LOWESS (Locally Weighted Regression)

Fits small local regressions across data
Produces smooth curves
Can be extended to multiple predictors

2️⃣ Kernel Regression

Uses weighted averages of nearby observations
Smooths complex relationships

3️⃣ Spline Regression (when highly flexible)

Uses piecewise curves joined at knots
Allows non-linear relationships
(Some spline models are semi-parametric)

4️⃣ Generalised Additive Models (GAMs)

Very important clinically
Combine multiple predictors with smooth, flexible functions
Often used in epidemiology

5️⃣ Decision Tree Regression / Random Forest Regression

No distributional assumptions
Handle complex, non-linear interactions
Common in modern clinical prediction modelling

🩺 Clinical Examples

1️⃣ Age, BMI & Cognitive Decline

Outcome:

Cognitive score

Predictors:

Age
BMI
Vascular risk score

Suppose:

Decline accelerates sharply after 75
BMI has non-linear effects

A non-parametric model can capture those curves without forcing linearity.

2️⃣ Drug Dose, Renal Function & Side Effects

Outcome:

Side effect severity

Predictors:

Dose
Age
Creatinine

The relationship may:

Increase sharply at mid doses
Plateau later

Non-parametric regression models that curve.

3️⃣ ICU Mortality Prediction

Outcome:

Mortality risk

Predictors:

Age
Lactate
Blood pressure
Comorbidities

Relationships are rarely linear — tree-based or GAM models often perform better.

👶 10-Year-Old Explanation

Imagine you’re drawing a road through dots again.

Parametric regression says:

> “The road must be flat and straight.”

Non-parametric multiple regression says:

> “The road can twist, turn, and curve to follow the dots — even in 3D.”

It doesn’t decide the shape first.
It figures it out from the data.

🧠 When Would You Use It?

Use non-parametric multiple regression when:

Relationship looks curved or complex
Interactions are likely
Linear assumptions are violated
You have a large dataset

Often used in:

Epidemiology
Biostatistics
Machine learning clinical prediction models

🎯 Important Clarification

This is different from:

Spearman correlation
Mann–Whitney test
Kruskal–Wallis

Those compare groups or ranks.
Non-parametric regression is about prediction/modelling.

⚡ Ultra-Short Exam Summary

Non-parametric multiple regression refers to flexible modelling techniques that estimate relationships between one outcome and multiple predictors without assuming a fixed linear form or normal residuals, allowing complex, data-driven associations.

🧠 Memory Hook

Parametric regression = 📏 rigid table

Non-parametric regression = 🧵 stretchy fabric that molds around the data

If the real world bends, the model should bend too.

CAP 2.2: Statistical Test Types (REVISE) Flashcards

(23 cards)