Kvant - cheatsheet

Question 1

Power (1 - β)

Answer 1

The probability of correctly rejecting H₀ when H₁ is true.

Question 2

2. Steps in Hypothesis Testing:

Answer 2

1. State the Hypotheses:
   H₀: No effect/difference.
   H₁: There is an effect/difference.
2. Select Significance Level (α):
   Common choices: 0.01, 0.05, 0.10.
3. Choose Test Type:
   One-Tailed Test: Tests for an effect in one direction (greater than or less than).
   Two-Tailed Test: Tests for an effect in both directions (not equal to).
4. Calculate the Test Statistic:
   Depends on the test being used (z-test, t-test, etc.).
5. Determine the p-value:
   Compare it to α.
6. Make a Decision:
   If p-value ≤ α, reject H₀.
   If p-value > α, fail to reject H₀.
7. Draw a Conclusion:
   Relate the decision back to the context of the problem.

Question 3

Types of Tests

Answer 3

1. Z-Test
2. T-Test
   Types:
   One-Sample T-Test
   Two-Sample T-Test
3. Chi-Square (χ²) Test
   Types:
   Goodness of Fit:
   Test of Independence:
4. ANOVA (Analysis of Variance)
5. Correlation and Regression Tests:
   Correlation Coefficient Test (pearson correlation)
   Linear Regression Test

Question 4

Correlation coefficient test and linear Regression Tests

Answer 4

Correlation Coefficient Test:
Pearson correlation. Tests if two variables are correlated.

Measuring linear correlation. Value from -1 to 1. Measures the direction and strenght of the relationship between to variables (continous)

Linear Regression Test: Tests if there is a linear relationship between variables.

Used to predict the value of a variable based on the value of another variable

Question 5

Decision rules

Answer 5

Two-Tailed Test:
- H₀: μ = μ₀, H₁: μ ≠ μ₀.
- Reject H₀ if |test statistic| > critical value.

One-Tailed Test (Right or Left):
- H₀: μ ≤ μ₀ (right-tailed) or μ ≥ μ₀ (left-tailed).

• right tailed: population parameter greater than a certain value. Fx more than 100 g.
  Reject H₀ if test statistic > critical value-

Left tailed: - population parameter less than a certain value. Fx less than 100 g. of chips.

test statistic < critical value (left-tailed).

Question 6

Common Significance Levels (α):

Answer 6

α = 0.10: Weak evidence.
α = 0.05: Standard threshold.
α = 0.01: Strong evidence.

Question 7

Distributions

Answer 7

Normal distribution: symmetric around the mean: the tails are equal
T-distribution: similar to a normal distribution but has heavier tails (more extreme values)
Chi-square distribution: asymmetric: tails are not equal due to its skewness