HYPOTHESIS TESTING Null Hypothesis and Research Hypothesis ?
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Transcript of HYPOTHESIS TESTING Null Hypothesis and Research Hypothesis ?
Null Hypothesis andResearch Hypothesis
HYPOTHESIS TESTING
?
The Null Hypothesis (Ho) The null hypothesis
– relates to a statistical method of interpreting conclusions about population characteristics that are inferred from observations made with a sample
– asserts that observed differences or relationships merely result from chance errors inherent in the sampling process
If the researcher rejects the null hypothesis– she accepts the research hypothesis– concluding that the magnitude of difference between
observed and anticipated is too great to attribute to sampling error
The Null Hypothesis (Ho) Operational Definition:
– MATH KNOWLEDGE score obtained on the Stanford Diagnostic Test - Level -
Brown– MATH SKILLS PRACTICE
number of problems completed on drill-and-practice work sheets
H0– There will be no difference in Math Knowledge scores for
students who practice and students that do not practice
The Research Hypothesis (H1) The research hypothesis
– is a formal affirmative statement predicting a single research outcome
– a tentative explanation of the relationship between two or more variables
– is directional In behavioral sciences
– the variables may be abstractions that cannot be directly observed
– these variables must be defined operationally by describing some sample of actual behaviors that are concrete enough to be observed directly
The Research Hypothesis (H1) Operational Definition:
– MATH KNOWLEDGE score obtained on the Stanford Diagnostic Test - Level -
Brown– MATH SKILLS PRACTICE
number of problems completed on drill-and-practice work sheets
H1– Math Knowledge scores will be higher for students that
practice
Possible Outcomes inHypothesis Testing
True False
Accept
Reject
Correct
CorrectError
Error
Errors: Type I and Type II• Type I error
– A type I error, also known as an error of the first kind, occurs when the null hypothesis (H0) is true, but is rejected. It is asserting something that is absent, a false hit. A type I error may be compared with a so called false positive (a result that indicates that a given condition is present when it actually is not present) in tests where a single condition is tested for. Type I errors are philosophically a focus of skepticism and Occam's razor. A Type I error occurs when we believe a falsehood.[1] In terms of folk tales, an investigator may be "crying wolf" without a wolf in sight (raising a false alarm) (H0: no wolf).
– The rate of the type I error is called the size of the test and denoted by the Greek letter (alpha). It usually equals the significance level of a test. In the case of a simple null hypothesis is the probability of a type I error.
– "convicting an innocent person" – NASA throw out suspected electric circuit
• Type II error– A type II error, also known as an error of the second kind, occurs when the null hypothesis is false, but it is
erroneously accepted as true. It is failing to assert what is present, a miss. A type II error may be compared with a so-called false negative (where an actual 'hit' was disregarded by the test and seen as a 'miss') in a test checking for a single condition with a definitive result of true or false. A Type II error is committed when we fail to believe a truth.[1] In terms of folk tales, an investigator may fail to see the wolf ("failing to raise an alarm"; see Aesop's story of The Boy Who Cried Wolf). Again, H0: no wolf.
– The rate of the type II error is denoted by the Greek letter (beta) and related to the power of a test (which equals ).
– What we actually call type I or type II error depends directly on the null hypothesis. Negation of the null hypothesis causes type I and type II errors to switch roles.
– The goal of the test is to determine if the null hypothesis can be rejected. A statistical test can either reject (prove false) or fail to reject (fail to prove false) a null hypothesis, but never prove it true (i.e., failing to reject a null hypothesis does not prove it true).
– "letting a guilty person go free“
Possible Outcomes inHypothesis Testing
True False
Accept
Reject
CorrectDecision
CorrectDecisionError
Error
Type I Error
Type II Error
Type I Error: Rejecting a True HypothesisType II Error: Accepting a False Hypothesis
Actuality
Sampling
Mean & Standard Deviation by Number of Dice Throws
# Throws MEAN S.D.10,000 7.0000 2.4157 5,000 7.0072 2.4360 1,000 7.0460 2.4300 500 7.0480 2.3040 100 7.6400 2.4599 50 6.6400 2.1453 25 6.9200 2.5807
Sample MEAN S.D.
25,000 67.993 1.902
20,000 67.984 1.900
15,000 67.997 1.903
10,000 67.986 1.900
5,000 67.965 1.884
1,000 67.998 1.915
500 67.922 1.907
100 68.182 1.653
50 68.037 2.010
25 67.633 1.965
Effect of Sampling on Mean & Standard DeviationHeight: U.S. Women
Random Samples of Population = 10,000 scores (0 to 99)
SAMPLE MEAN s.d.
10 54.80 32.1920 58.45 27.1430 54.63 30.2750 49.14 29.59
100 47.09 29.76200 47.05 28.84500 48.00 28.73
1,000 50.15 28.992,000 49.45 29.035,000 49.48 28.96
10,000 49.57 28.97
Probability Sampling: every member of the population has a nonzero probability of being selected for the sample
Random Selection and Random Assignment: used to obtain representativeness and eliminate possible bias
Concept of Random Sampling
34%
14%2%
67.99 69.89 71.7966.0964.19
67.99 69.89 71.7966.0964.19
5772.3%
3,36113.4%
8,53234.1%
8,54734.2%
3,41913.7%
5642.6%
PopulationIntact GroupServing asSample
Representativenessestablished on logical basis
Random Assignment
ExperimentalTreatments
Results Generalized
Population SampleRandom SampleMeasured
Results GeneralizedRandom Selection
Contrast Between Random Selection and Random Assignment
Types of Random Sampling Simple Random Sampling
– all individuals in a population have equal probability of being in sample
All populations are made up of many subpopulations: race, gender, age group, geographic region, etc.
Stratified Random Sampling–sampling fraction
ratio of sample size to population size
–sub populations (strata) are identified–individuals are randomly chosen from each strata using: equal, proportional, or optimal allocations
Race - Black Geographic
Region - West
Geographic Region - East
Race - White
Three Types of Allocation EQUAL
– all strata contribute the same number to the sample
PROPORTIONAL– Sample allocation is proportional to the strata
population size
OPTIMUM– Sample allocation is proportional to the product of
the strata population sizes and variability
Cluster Sampling When the selection of individuals of the
population is impractical:– a procedure of selection in which the unit of
selection (cluster) contains two or more population members
Population of 4thgrade classes:83 classes in 33 schools
Random selectionof classes
Sample of 20classes (561 students)
All members of these20 classes are usedas sampleResults
Generalized
Nonrandom Sampling Systematic Sampling
– every nth individual in the population is selected– sampling interval
Convenience Sampling– a group of individuals available to study
Purposive Sampling– selection based on prior knowledge of researcher