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Statistics in Behavioral Sciences - Coggle Diagram
Statistics in Behavioral Sciences
Statistics in Behavioral Sciences
Core Purpose of Inferential Statistics
Use sample data to make conclusions about populations
Help researchers test hypotheses
Support decision-making under uncertainty
Chapter 7: Central Limit Theorem (CLT)
Central Limit Theorem Definition
Distribution of sample means becomes normal as sample size increases
Works even if population is not normal
Sampling Distribution
Distribution of sample means
Based on repeated samples
Becomes more normal with larger n
Effect of Sample Size
Larger samples reduce variability
Smaller samples produce more variation in means
Mean of Sampling Distribution
Equals population mean (μ)
Standard Error
Standard deviation of sample means
Measures variability of sample means
Decreases as sample size increases
Real-World Application in Education
Test score averages across classrooms
Different classes represent different samples
Helps compare school performance fairly
Why CLT Matters
Makes non-normal data usable for analysis
Allows use of normal distribution techniques
Simplifies probability calculations
Relationship to Normal Distribution
Sample means approach normal shape
Enables inference using z-scores
Limitation Understanding
Works best with sufficiently large samples
Small samples may not approximate normality well
Chapter 8: Hypothesis Testing
Null Hypothesis (H0)
Assumes no effect or no difference
Assumes results are due to chance
Serves as default position
Alternative Hypothesis (H1)
Assumes an effect or difference exists
Research hypothesis
What researcher tries to support
Purpose of Hypothesis Testing
Evaluate evidence from sample data
Make decisions about population claims
Reduce uncertainty in conclusions
Decision Outcomes
Reject H0 when evidence is strong
Fail to reject H0 when evidence is weak
Type I Error
Rejecting a true null hypothesis
False positive
Type II Error
Failing to reject a false null hypothesis
False negative
Real-World Example in Medicine
Testing new drug effectiveness
Null: drug has no effect
Alternative: drug improves condition
Importance of Distinction
Prevents misinterpretation of results
Avoids assuming “no evidence” means “no effect”
Common Misunderstanding
Failing to reject H0 ≠ proving H0 is true
Decision Depends on Alpha Level
Common alpha = .05
Defines rejection region
Chapter 9: t Statistics and t Tests
When t Statistic is Used
Population standard deviation unknown
Standard deviation estimated from sample
z Test vs t Test
z test uses known population standard deviation
t test uses estimated standard deviation
Why t Statistic is Important
More realistic for real research situations
Accounts for uncertainty in estimation
t Distribution Shape
Wider and flatter than normal distribution
More spread when sample size is small
Approaches normal as sample size increases
Degrees of Freedom
Based on sample size
Affects shape of t distribution
Standard Error in t Test
Uses sample standard deviation
Estimates population variability
Real-World Example in Psychology
Measuring stress before and after therapy
Comparing two conditions using sample data
Real-World Example in Education
Testing new teaching method effectiveness
Comparing sample classroom results
Importance of t Tests
Allows inference without full population data
Common in behavioral science research
Relationship to Hypothesis Testing
Used to test H0 vs H1
Produces t statistic for decision-making