Learning Objectives
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# Learning Objectives - Apply descriptive and inferential statistics - Conduct and interpret hypothesis tests - Choose appropriate statistical tests - Statistics fundamentals (mean, variance, normal distribution) - Weeks 1-4: Research design and data collection ## 1. Descriptive Statistics **Central Tendency:** Mean...
Learning Objectives
- Apply descriptive and inferential statistics
- Conduct and interpret hypothesis tests
- Choose appropriate statistical tests
- Statistics fundamentals (mean, variance, normal distribution)
- Weeks 1-4: Research design and data collection
1. Descriptive Statistics
Central Tendency: Mean (average), Median (middle value), Mode (most frequent). Mean is sensitive to outliers, median is robust.
Dispersion: Range (max-min), Variance (average squared deviation), Standard Deviation (square root of variance). Std dev has same units as data.
Distribution Shape: Skewness (asymmetry), Kurtosis (tail thickness). Normal distribution: skew=0, kurtosis=3.
2. Hypothesis Testing Framework
Steps:
- H0 (null hypothesis - no effect) and H1 (alternative - there is an effect)
- Significance level (alpha = 0.05 standard)
- Select and compute test statistic
- Determine p-value (probability of observing data if H0 is true)
- If p < alpha: REJECT H0 (evidence for H1). If p >= alpha: FAIL TO REJECT H0 (not enough evidence) Type I Error: Rejecting true H0 (false positive). Alpha = probability of Type I error. Type II Error: Failing to reject false H0 (false negative). Beta = probability of Type II error. Power: 1 - Beta = probability of correctly rejecting false H0.
3. Common Statistical Tests
| Test | Purpose | Example |
|---|---|---|
| t-test (independent) | Compare means of 2 independent groups | Men vs women satisfaction |
| t-test (paired) | Compare means of same group at 2 times | Pre vs post campaign |
| ANOVA | Compare means of 3+ groups | Satisfaction by region (North, South, East, West) |
| Chi-square | Association between 2 categorical variables | Gender and brand preference |
| Correlation | Strength of linear relationship | Advertising spend and sales |
Q1: When to use t-test vs ANOVA?t-test: exactly 2 groups. ANOVA: 3 or more groups. Both compare means. If ANOVA is significant, follow with post-hoc tests to identify which pairs differ. Q2: What is the difference between Type I and Type II error?Type I: false positive (reject true H0). Example: conclude drug works when it doesn't. Type II: false negative (fail to reject false H0). Example: conclude drug doesn't work when it does. Q3: What is p-value? How is it interpreted?Probability of observing data as extreme as actual, assuming H0 is true. p < 0.05: statistically significant (reject H0). p > 0.05: not significant (insufficient evidence to reject H0). Q4: When to use chi-square test?Testing association between two categorical variables. Example: Is there a relationship between education level (high school, bachelor, master) and brand preference (A, B, C)? Q5: What does "statistically significant" mean?It means the observed difference is unlikely to have occurred by chance alone (given alpha = 0.05). It does NOT mean the difference is practically important or large in magnitude. Join Discord PreviousQualitative Research MethodsNextFactor Analysis