Final Exam

📊 Descriptive Statistics = “describe your data”

👉 Just summarizing your sample (NOT testing anything)

📍 Measures of Central Tendency (the center)

• Mean → average

• Median → middle value

• Mode → most common value

📉 Measures of Dispersion (spread)

👉 How spread out your data is

• Variance → spread (squared distances from mean)

• Standard Deviation (SD) → average distance from mean

• Standard Error (SE) → how accurate your sample mean is

🔥 EASY WAY TO REMEMBER

• Mean = center

• SD = spread

• SE = accuracy of mean

🧪 Super simple example:

If test scores are:
👉 80, 82, 85

• Mean ≈ 82

• SD = how far scores are from 82

• SE = how confident we are that 82 represents the population

🧠 Inferential Statistics = “make conclusions”

👉 You use a sample
👉 To make claims about the population

🔑 NHST (Null Hypothesis Significance Testing)

👉 You test:

• H₀ (null) = no effect

• H₁ (alternative) = there is an effect

👉 Then check p-value

🧪 Types of Designs

🔗 Correlational

👉 Looks at relationship between 2 variables

• Example: stress & sleep

🧬 Experimental / Pseudo-experimental

👉 Looks at cause and effect

• Has:

  • IV (what you change)

  • DV (what you measure)

📊 Variable Types

Binary

👉 2 options

• e.g., yes/no

Categorical

👉 Groups

• Nominal = no order

  • e.g., gender, color

• Ordinal = ordered

  • e.g., rankings (1st, 2nd, 3rd)

Continuous

👉 Measured on a scale

• e.g., height, grades, time

⚠ Alpha Level (α)

👉 Usually: α = .05

👉 This means:

🔥 Decision rule (VERY IMPORTANT)

• p ≤ .05 → significant ✅

• p > .05 → not significant ❌

🧠 One-line summary:

👉 Inferential stats = use sample data + p-values to decide if results apply to the population.

🔵 F-value (ANOVA table)

👉 Big picture: does the model work?

• Tests the overall model

• Asks:

  “Does X predict Y at all?”

✅ If p < .05:

👉 The model is significant
👉 There is a relationship between X and Y

❌ If p > .05:

👉 The model does not predict Y

🟣 t-value (Coefficients table)

👉 Zoomed in: does this predictor matter?

• Tests each predictor individually

• Asks:

  “Does THIS variable help predict Y?”

✅ If p < .05:

👉 That predictor significantly contributes

❌ If p > .05:

👉 That predictor does not contribute

🔥 EASY WAY TO REMEMBER

👉 F = Full model
👉 t = Each term (predictor)

🧪 Example

If:

• F is significant ✅

• but one predictor has p > .05 ❌

👉 That predictor is useless, even though the model works overall

🧠 One-line summary (exam gold):

👉 The F-test evaluates the overall model, while the t-test evaluates the significance of individual predictors.

🚨 Super important connection:

• F test → “Does anything matter?”

• t test → “Which things matter?”

🧠 Why do we get BOTH b and β?

👉 Because they answer two different questions

🔵 Unstandardized (b)

👉 Used for prediction

• In original units (real numbers)

• Goes into the equation:

  Y^=b0+b1X1+b2X2\hat{Y} = b_0 + b_1X_1 + b_2X_2Y^=b0​+b1​X1​+b2​X2​

💡 Meaning:

🧪 Example:

• b = 2
  👉 If study time increases by 1 hour → grade increases by 2 points

🟣 Standardized (β)

👉 Used for comparison

• Converted to z-scores (standard deviations)

• No units → everything on same scale

💡 Meaning:

🔥 Why is β useful?

👉 Lets you compare predictors:

Example:

• Study time: β = .50

• Sleep: β = .20

👉 Study time is the stronger predictor

🚨 When do we care about β?

👉 ONLY when:

• You have multiple predictors

• AND more than one is significant (p < .05)

🔑 EASY WAY TO REMEMBER

👉 b = build equation
👉 β = best predictor

🧠 One-line summary:

👉 Unstandardized coefficients (b) are used to make predictions, while standardized coefficients (β) are used to compare the relative importance of predictors.

🚨 Exam tip

If they ask:

• “Write the equation” → use b

• “Which predictor is strongest?” → use β

🧠 One-tailed vs Two-tailed (BIG idea)

🔵 One-tailed test

👉 You care about ONE direction only

💡 Example:

• “Home scores are higher than park”

• HA: μHome > μPark

👉 You are only testing one side

🟣 Two-tailed test

👉 You care about ANY difference

💡 Example:

• “Home and park are different”

• HA: μHome ≠ μPark

👉 Could be higher OR lower

🔥 EASY WAY TO REMEMBER

👉 Directional = one-tailed
👉 Non-directional = two-tailed

📊 What SPSS gives you

👉 SPSS always gives:
➡ Two-tailed p-value

🔑 If you want one-tailed:

👉 Divide p by 2

⚠ ONLY if:

• Your hypothesis was directional from the start

🚨 Important warning (EXAM TRAP)

👉 You cannot decide after seeing results

❌ Don’t say:

👉 Must decide before analysis

🧪 Example:

If SPSS gives:

• p = .04 (two-tailed)

👉 One-tailed:

• p = .02

🧠 One-line summary:

👉 One-tailed tests examine a specific direction, while two-tailed tests examine any difference regardless of direction.

🔥 Quick cheat sheet

🧠 What is a Post Hoc test?

👉 A follow-up test after ANOVA

🔑 Why do we need it?

👉 ANOVA tells you:

👉 BUT it does NOT tell you:

🔥 So post hoc tests answer:

👉 Which specific groups are different

🧪 Example (3 groups)

If you have:

• L1, L2, L3

Post hoc compares:

• L1 vs L2

• L1 vs L3

• L2 vs L3

🚨 IMPORTANT RULE

👉 Only do post hoc tests if:

👉 ANOVA is significant (p < .05)

❌ If ANOVA is NOT significant:

👉 STOP
👉 Do NOT run post hoc tests

🧠 One-line summary:

👉 A post hoc test is conducted after a significant ANOVA to determine which specific group differences are significant.

🔥 EASY MEMORY TRICK

👉 ANOVA = “something is different”
👉 Post hoc = “what is different”

🧠 What is Effect Size?

👉 Tells you how big the effect is
👉 NOT just if it’s significant

🔑 Why it matters:

• p-value → “Is it real?”

• Effect size → “How strong is it?”

🧪 For t-tests → Cohen’s d

Interpretation:

• d = 0.20 → small (barely noticeable)

• d = 0.50 → medium (noticeable)

• d = 0.80+ → large (strong effect)

📊 For ANOVA → Eta squared (η²)

👉 Tells you:

Interpretation:

• .01 → small

• .06 → medium

• .14 → large

🔍 Difference:

• η² (eta squared) → total variance explained

• partial η² → variance explained controlling for other variables

🔥 EASY WAY TO REMEMBER

👉 d = difference (t-test)
👉 η² = variance explained (ANOVA)

🧠 One-line summary:

👉 Effect size measures the strength of a relationship or difference, independent of statistical significance.

🚨 Exam tip:

👉 You can have:

• significant result + small effect
  👉 OR

• non-significant + large effect (small sample)

🧪 Example:

If:

• p < .05

• d = 0.80

👉 Significant AND strong effect

🟦 THE 4 STEPS (EASY VERSION)

1. 🏷 Label (name the factor)

👉 Give it a name that describes the variables

Example:

• Variables: happy, joyful, excited
  → Factor name = Positive Emotion

2. 📊 Loadings (what loads strongly?)

👉 Look for high loadings (usually > .40 or .50)

Example:

• happy (.80)

• joyful (.75)

• excited (.70)

👉 These define the factor

3. ➕➖ Direction

👉 Are loadings positive or negative?

• Positive → variables increase together

• Negative → opposite meaning

Example:

• happy (+)

• sad (−)

👉 Factor might be Emotional Valence

4. 🧠 Interpret (explain it)

👉 WHY did you name it that?

Example:
👉 “This factor was labeled Positive Emotion because items related to happiness and excitement loaded strongly and positively.”

🧪 FULL EXAMPLE (EXAM STYLE)

Given:

✅ Answer:

Label: Positive Emotion
Loadings: happy, joyful, excited (positive); sad (negative)
Direction: Mostly positive, with one negative loading
Interpretation: This factor reflects emotional positivity, as positive emotions load positively and sadness loads negatively.