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Free Measures Theory Testing Unit 8 Ch 10: 1-5, 7, 9, 11, 13, 15, 19 (pp. 282-286) Looking at 2 sets of information 2 general examination systems information sets originate from 2 separate gatherings free examples between gatherings plan 2 sets of information from 1 bunch needy or related specimens

Transcripts

Autonomous Measures Hypothesis Testing Unit 8 Ch 10: 1-5, 7, 9, 11, 13, 15, 19 (pp. 282-286)

Comparing 2 sets of information 2 general exploration procedures information sets originate from 2 separate gatherings autonomous examples between gatherings outline 2 sets of information from 1 bunch needy or related specimens coordinated subjects (2 related gatherings) inside of subjects configuration ~

Independent Measures Hypothesis Test Select 2 free specimens would they say they are from same populace? Examination select 2 tests 1 gets treatment are the specimens the same? ~

Experimental Outcomes Do not hope to be precisely equivalent testing blunder How huge a distinction to reject H 0 ? ~

Hypotheses: Independent Measures Nondirectional H 0 : m 1 - m 2 = 0 H 1 : m 1 - m 2 ï¹ 0 or H 0 : m 1 = m 2 H 1 : m 1 ï¹ m 2 Directional (relies on upon forecast ) H 0 : m 1 - m 2 < 0 H 1 : m 1 - m 2 > 0 or H 0 : m 1 < m 2 H 1 : m 1 > m 2 no quality determined for either Group 1 scores = Group 2 scores ~

Sample measurement: t test: Independent Samples Same essential structure as single example Independent specimens [df = n 1 + n 2 - 2]

The Test Statistic Since m 1 - m 2 = 0 [df = n 1 + n 2 - 2]

Estimated Standard Error *Standard lapse of contrast between 2 test means must figure s 2 p first ~

Pooled Variance ( s 2 p ) Average of 2 test differences weighted normal if n 1 ï¹ n 2 if n 1 = n 2

The Test Statistic: Assumptions 1. Tests are free 2. Tests originate from typical populaces 3. Accept break even with change s 2 1 = s 2 does not oblige s 2 1 = s 2 homogeneity of fluctuation t test is strong infringement of suppositions Little impact on P(rejecting H 0 ) ~

Example: Independent Samples Is exam execution influenced by what amount of rest you get the night prior to a test? Subordinate variable? free variable? Grp 1: 4 hrs rest ( n = 6) Grp 2: 8 hrs rest ( n = 6) ~

Example: n 1 = n 2 1. State Hypotheses H 0 : m 1 - m 2 = 0 or H 0 : m 1 = m 2 H 1 : m 1 - m 2 Â¹ 0 or H 1 : m 1 Â¹ m 2. Set model for dismissing H 0 : nondirectional a = .05 df = (n 1 + n 2 - 2) = (6 + 6 - 2) = 10 t CV .05 =

Example: n 1 = n 2 3. select specimen, process measurements do investigation mean exam scores for every gathering Group 1: M 1 = 15 ; s 1 = 4 Group 2 : M 2 = 19; s 2 = 3 register s 2 p s M 1 - M 2 t obs ~

Example: n 1 = n 2 figure s 2 p

Example: n 1 = n 2 figure

Example: n 1 = n 2 figure test measurement

Example: n 1 = n 2 4. Choice? Is t obs in basic locale? No, neglect to reject H 0 If directional test or change level of essentialness change discriminating estimation of t ( t cv ) simply like different tests ~

Pooled Variance: n 1 Â¹ n 2 Unequal specimen sizes weight every fluctuation greater n - > more weight

Example: n 1 Â¹ n 2 Supplementary Material What impact does the measure of rest the night prior to an exam have on exam execution? Subordinate variable free variable Grp 1: 4 hrs rest ( n = 6) Grp 1: 8 hrs rest ( n = 7) ~

Example: n 1 Â¹ n 2 1. State Hypotheses H 0 : m 1 = m 2 or m 1 - m 2 = 0 H 1 : m 1 Â¹ m 2 or m 1 - m 2 Â¹ 0 2. Set measure for dismissing H 0 : nondirectional a = .05 df = (n 1 + n 2 - 2) = (6 + 7 - 2) = 11 t CV = + 2.201 ~

Example: n 1 Â¹ n 2 3. select specimen, process insights do test mean exam scores for every gathering Group 1: M 1 = 14 ; s 1 = 3 Group 2 : M 2 = 19; s 2 = 2 figure s 2 pooled s M 1 - M 2 t obs ~

Example: n 1 Â¹ n 2 register s 2 pooled figure test measurement [df = n 1 + n 2 - 2]

Example: n 1 Â¹ n 2 4. Decipher Is t obs past t CV ? In the event that yes, Reject H 0