1 / 20

PRINCIPLES OF HYPOTHESIS TESTING

PRINCIPLES OF HYPOTHESIS TESTING. Why Sampling?. A Quick Review of Important Issues About Sampling:. To examine the sample ’ s attributes ( sample statistics ) as ESTIMATES of the population ’ s characteristics ( population parameters )

timon-caldwell
Télécharger la présentation

PRINCIPLES OF HYPOTHESIS TESTING

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PRINCIPLES OF HYPOTHESIS TESTING

  2. Why Sampling? A Quick Review of Important Issues About Sampling: To examine the sample’s attributes (sample statistics) as ESTIMATES of the population’s characteristics (population parameters) use sample characteristics to make inferences about the population. Estimating, by definition, involves some error (i.e., sampling error/bias Resulting from the fact that the sample may not mirror characteristics of the population).

  3. HYPOTHESIS TESTING OFTEN INVOLVES: • comparing groups regarding differences in means or proportions, or • Examining strength and direction of relationships between two variables Common Types of Research Hypotheses and the Related Statistical Data Analysis Methods: • Checking for Presence/Absence of Relationship(s) Among Variables (and direction/strength of the relationship) • Bivariate (e.g., Pearson Correlation—r) • Between one variable and another: Y = a + b1 x1 • Multivariate (e.g., Multiple Regression Analysis) • Between one dep. var. and an independent variable,while holding all other independent variables constant: Y = a + b1 x1 + b2 x2 + b3 x3 + … + bk xk • Checking for Presence/Absence of Difference(s) Among Groups • Difference(s) in Proportions (Chi Square Test—2) • Difference(s) in Means (Analysis of Variance)

  4. HYPOTHESIS TESTING QUESTION: When testing hypotheses regarding presence of a relationship/ difference, what does “NULL HYPOTHESIS” (H0) refer to? • Null Hypothesis in most cases states: • “There is no relationship or no difference.” • If we reject the null, the conclusion is that we have found a statistically significant relationship/difference. • When we don’t reject the null, we infer that . . .?“…any difference/relationship that may be apparent from sample data is likely to be the result of . . .?? • NOTE:Statistical tests of hypotheses always report the result of testing the null hypothesis. • The researcher will then have to restate the results in terms of finding/not finding support for the original research hypothesis. • sampling error (i.e., an artifact of the particular samplebeing used)”.

  5. A Quick Review of Important Issues About Sampling: • So, when using sample data to test hypothesesand make judgments about the population, there is always a chance for reachingerroneous conclusionsabout the population. • What do we mean by erroneous conclusions? • What types of erroneous conclusions can we reach when testing hypotheses?

  6. Important Notes About Sampling • Two possible types of erroneous conclusions from sampling error, when testing hypotheses: TYPE I ERRORand TYPE II ERROR

  7. Important Notes About SamplingType I Error? • Rejecting a true“null hypothesis” (erroneously) • Rejecting the null when we should not (i.e., when the null is true) Null Hypothesis? • States “There is NO relationship, there is NO difference, etc.” • “Rejecting the null” refers to concluding…? • Concluding that: “There is a significant relationship/ difference”

  8. Important Notes About Sampling So, type I error (“Rejecting a True Null”) means? • No relationship/difference exists, but from sample evidence we come to the conclusion that a significant relationship/ difference does exist. • Example: A drug is really not effective, but we conclude it is. • Conclusion: Type I Error involves finding “something” that does not really exist—i.e., a case of “False positive” Sample

  9. Important Notes About SamplingType II Error? • Accepting a false null hypothesis (or failing to reject a false null hypothesis) False Null means? • “A relationship/difference does in fact exist”. So, “accepting a false null” (i.e., type II error) means? • A relationship/difference does in fact exist, but from sample evidence we fail to detect it (fail to reject the null). • Come to the conclusion that there is no relationship/difference (in the population). • Example; A drug is really effective, but our study shows it is not.

  10. Important Notes About SamplingType II Error: CONCLUSION: Type II Error represents failing to find “something” that does exist; it represents a case of “False Negative.” Sample

  11. A Quick Review of Important Issues About Sampling: • Statistical tests of significance assess the likelihood of reaching anerroneous conclusion when using sample data. In fact, they always assess the likelihood of type I error. • They assess the probability that the relationship/ difference we have found (using sample data) may simply be an artifact of the particular sample we have happened to end up with (i.e., is caused by sampling error). • In fact, when using data from the entire population (e.g., a census): • No chance of sampling error exists • No need for conducting statistical tests of significance. When testing hypotheses, what is the purpose of statistical testing (significance testing)?

  12. HYPOTHESISTESTING • Statistical tests of significance alway assessthe likelihood/probability of type I error (a)when using sample data. • Once a test is conducted and a is determined, we willhave to decide if we are able/willing to tolerate a (the riskinvolved in rejecting the null(and, thereby, to report what…?) • … that the relationship/difference detected (from sample data), istoo large to be attributed to chance/sampling error. • That is, decide whether we should consider the relationship/difference “statistically significant.” Sample

  13. Important Notes About Sampling • The probability of committing Type I Error is called: • (alpha) or significance level. The complement of : • 1-  or confidence level. What does 1-  represent? • probability of accepting (not rejecting) the null when it is true: • concluding NO relationship/difference exists, when indeed it DOES NOT exist (i.e., chance of not finding what does not exist)—a correct conclusion

  14. HYPOTHESIS TESTING • So, testing the plausibility of hypothesis/propositions (i.e., decision to reject/not reject H0) is a probabilistic decision...? • It requires us to: • Determinethe likelihood of null being true (a) and, thus, the risk (of being wrong) that we would be taking if we decide to reject the null(a), and • Decide whether we are willing/able to tolerate that risk (alevel) by actually rejecting the null… • and reporting that we have found a“significant” relationship/difference. • So, generally speaking, when should we betempted to reject the null?When (a) is ___large or when it is ___small?

  15. HYPOTHESISTESTING • A small a means that… • …the CHANCE of NULL being TRUE is TOO SMALL to warrant ACCEPTING it . • …if we decide to reject the null (i.e., conclude that we have found a relationship/difference), we standa relatively small chance of being wrong. • …rejecting the null is a relatively safe bet. • …the difference/relationship found is statistically significant . • NOTE: • Small a rejecting the null finding a statistically significantrelationship/difference reporting that the relationship/differencefound (from sample evidence) is too large to be attributed to chance/sampling error

  16. HYPOTHESIS TESTING BUT HOW DO YOU MEASURE a? • How would you determine what the actual alevel is (i.e.,how much risk of being wrong you would actually be taking if you were to decide to reject the null? • ANSWER… • Look up the actual a from a table of probability distribution for the test statistic being used, OR (b) More conveniently, rely on your statistical software (e.g., SPSS) to compute and report the actual a (“Sig.” or “Prob.”) level for you.

  17. HYPOTHESIS TESTING DECIDING ON AN athat I CAN TOLERATE!!! • BUT, WAIT ... How am I supposed to know what oddsof being wrong I should be willing/able to tolerateas I consider rejecting the null? • A SIMPLE ANSWER: a< 5% is conventionallyconsidered to be areasonable/small enough risk to be tolerable in most situations.

  18. HYPOTHESIS TESTING • IS THERE A RULE OF THUMBTO FOLLOW WHEN TESTING HYPOTHESIS? YES! • WHAT IS IT? • THE GOLDEN RULE: When testing a hypothesis, • if the reported a (e.g., “sig.” in SPSS) turns out tobe less than or equal to 0.05, reject the null and report a statistically significant relationship/difference • Because the odds of being wrong would be tolerable). • Otherwise, refrain from rejecting the null, on the grounds that the odds of committing an error (i.e., rejecting a true null) would be prohibitive. • And, as a result, report . . . ?

  19. HYPOTHESIS TESTING • Use a smaller a (e.g., a< 0.01 ) when: • Sample size is relatively large • Consequence of committing type I error is serious/costly (i.e., False positive results are very costly) • (e.g., H0: Capital punishment is not a strong deterrentfor criminal behavior.) • Use a larger a (e.g., a< 0.10 ) when: • Sample size is relatively small • Conducting exploratory research whose results provide the basis for further research EXCEPTIONS TO THE RULE?

  20. HYPOTHESIS TESTING QUESTIONS OR COMMENTS ?

More Related