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Statistics - Coggle Diagram
Statistics
Percentiles and Quartiles
Percentile
-score corresponding to a rank
Quartiles:
Q1
-25th percentile
Q2
=50th percentile(median)
Q3
=75th percentile
Percentile Rank
-% of scores ≤ X
Interquartile Range (IQR)
=Q3-Q1
Errors in Hypothesis Testing
α =
probability of Type I
Type II Error (β):
fail to reject false H₀
β influenced by:
α level
effect size
sample size
Type I Error (α)
: reject true H₀
Probability
-outcome as part of a whole
Probability Values
0 (0%)
=never occurs
1 (100%) =
always occurs
Proportion
Expressed as fractions or percentages
Sampling
Independent Random Sampling
Constant probabilities
Sampling with replacement
Without Replacement
Common, but probabilities change
Random Sampling
=chance for all
Z-Scores and Unit Normal Table
Used for normal distributions only
Unit Normal Table Columns:
A:
z-Scores
B:
Proportion in body
C:
Proportion in tail
D:
Between mean and z
Z-Score:
Transforms X into standard units
Central Limit Theorem (CLT)
SD
= σ/√n = Standard Error (σM)
Normal shape if:
n ≥ 30
Population is normal
Mean
= μ
Sampling Distributions
Distribution of Sample Means
-All possible sample means from population
Sampling Distribution
-Distribution of stats from samples
Sampling Error
-Difference between sample stat and population parameter
Three Interrelated Distributions
:
Sample
=selected group
Sampling Distribution:
=M values
Populations
=all individuals
Significance and Critical Region
Critical Region:
sample values that lead to rejecting H₀
Statistical Significance:
data falls in critical region
Alpha Level (α):
defines “very unlikely”
Test Statistic
Measures difference between observed M and expected μ
Large z
= evidence against H₀
z-Score Formula:
z=M-μ/σM
Effect Size (Cohen’s d)
d=M-μ/𝜎
Independent of sample size
Measures size of treatment effect
Statistical Power
-Probability of detecting a real effect (rejecting false H₀)
Decreased by:
Lower effect size
Smaller α
Increased by:
Higher effect size
One-tailed test
Larger sample size
Power Analysis
: Done before the study to determine needed sample
Standard Error
Affected by:
Sample size
Population SD
Measures:
How well M represents μ
Variability of sample means
One-Tailed vs. Two-Tailed Tests
One-Tailed:
All in one tail
H₁: μ > μ₀ or μ < μ₀
Requires directional prediction
Two-Tailed
Critical regions in both tails
H₁: μ ≠ μ₀
Overview of Hypothesis Testing
-uses sample data to test population claims
Four Steps
2
: set α and find critical region
3
: collect data & compute z
1
: state H₀ and H₁
4
: Make a decision (reject or fail to reject H₀)