Z-Test and T-Test

301 views
279 views

Published on

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
301
On SlideShare
0
From Embeds
0
Number of Embeds
43
Actions
Shares
0
Downloads
4
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Z-Test and T-Test

  1. 1. Kelly Chan | Nov 19 2013 Z-Test & T-Test Formulas Process Mean ( distances)DifferenceBetweenMeans ( stdDev)StandardError Difference Mean 1 Z/T-Statistic StdDev Standard Error n Alpha: significance level Hypothesis 2 Z/TCriticalValue df: degree of freedom Decision 3 CI: Confidence Intervals CI =mean( X )±CriticalValue(Z/T )∗SE (StandardError) 2 r= t 2 t 2 +df 4 The proportion of a difference in means
  2. 2. Kelly Chan | Nov 19 2013 Z-Test & T-Test Z-Test Normal distribution Large sample size Population StdDev T-Test: Dependent T-Test: Independent Normal distribution Small sample size Population StdDev unknown One Category, One Item - Pre/Post Study - Longitudinal Study - Two-Conditions Study ∑ (x −mean (x ))2 One Category, Two Items - Observational Study - Experimental Study ∑ (x −mean (x ))2 n Study n−1 stdDev √ (n) x −mean (x ) StdDev n √ ( variance(AB)= √ variance (x1−x2) ) n−1 ( √ ( variance ( AB) variance( AB) + ) n( A) n (B) mean( A)−mean(B) mean (A)−mean (B)−ExpectedDifference(AB) variance( A) variance (B) + ) ( n( A) n (B) variance( AB) variance(AB) ( + ) n (A) n( B) mean (x1)−mean (x2) √ variance ( A) variance( B) + ) n ( A) n( B) √ variance(x1 −x2) ) ( n−1 n−1 n(A)+n(B)−2 t 2 r= variance ( A)+ variance( B) df ( A)+df ( B)−2 2 2 t +df CI =mean( X )±CriticalValue(Z/T )∗SE (StandardError) √ Variance Standard Error Z/T-Statistic df: degree of freedom The proportion of a difference in means CI: Confidence Intervals
  3. 3. Kelly Chan | Nov 19 2013 T-Test: Calculations Dependent Independent Mean mean (x1)−mean (x2) √ Difference Mean mean( A)−mean( B) √ variance(x1 −x2) ( ) n−1 variance( A) variance (B) ( + ) n( A) n (B) 1 T-Statistic StdDev Standard Error n Alpha: significance level Hypothesis 2 T-CriticalValue n−1 n(A)+n(B)−2 df: degree of freedom Decision 3 CI: Confidence Intervals CI =mean(X )±T −CriticalValue∗SE(StandardError) 2 r= t 2 t 2 +df 4 The proportion of a difference in means

×