By: Becca Doll, Stevie Lemons, Eloise Nelson

 Groups of five or fewer.  No looking at notes or readings.  You have one minute.  On scratch paper, write down as many key terms and concepts from this class as you can remember. Anything from the quarter.  There is a reward

 “Calculates the probability, p, that an observed difference between two or more data samples can be explained by random chance alone, as opposed to any fundamental difference between the underlying populations that the sample came from.” (

 1- Formulate null hypothesis (H₀) and research hypothesis (H₁/ H‸)‏ 2- Choose a sample distribution and a statistical test according to the null hypothesis and data type.  3- Specify a significance level (α) and define the region of rejection (Nachmias ©1992 ) How to construct a test

 4- Compute and reject/ fail to reject the null  5- Describe your findings in English. (Nachmias © 1992) Construction continued.

 Hypothesis testing is largely the product of Ronald Fisher, Jerzy Neyman, Karl Pearson and (son) Egon Pearson.  Fisher→ Rigorous experimental design to extract a result from few samples. Chi-square  Pearson→ Emphasized mathematical rigor and methods to obtain more results from many samples and a wider range of distributions. Pearson’s correlation (Wikipedia) A little History

 To formulate use The Principle of Parsimony or economy. ♫ A null hypothesis (H₀) is a statement made by a researcher at the beginning of an experiment that says, essentially, that nothing is happening in the experiment. ♫ The alternative also called the research hypothesis (H₁/ H‸) is the antithesis of the null. (Nachmias © 1992) Formulating Hypothesis

 The data collected from your sample population can be classified into one of four categories.  Nominal→ Yes/ No answer  Ordinal→ First, Second, Third Discrete scales, not continuous  Interval→ No true zero, like temperature  Ratio → True zero, like money  Once you know what kind of data you have you can choose the appropriate Statistical Test (Richardson) Sample distribution and Statistical Test

 “The decision as to what result is sufficiently unlikely to justify the rejection of the null hypothesis is quite arbitrary”  “The sum of the probabilities of the results included in the region of rejection is denoted as the level of significance (α)” ◦ The level is usually set at.05 or.01  Region of Rejection  “The area specified by a null hypothesis that covers the values of the observed statistics that lead to the rejection of the null hypothesis.”  (Nachmias © 1992) Significance level and Region of Rejection

 A statistical test can be one tailed or two.  “Two-tailed-region of rejection is located at both left and right tails.” ≠  “One-tailed- extreme results can be located at either tail.” (Nachmias © 1992) Region of Rejection continued

 Type I and Type II Errors (Nachmias © 1992) Reject or Fail to Reject the Null Type II errorNo errorAccept Hypothesis No errorType I errorReject Hypothesis Null Hypothesis is False Null Hypothesis is True Decision

(Rogers) Defendant InnocentDefendant Guilty Reject the Null Hypothesis Type I Error (innocent person convicted) Correct Fail to Reject the Null Hypothesis CorrectType II Error (guilty person goes free)

1) COURT CASE : H₀: The Defendant is not guilty 2) MANUFACTURING AIRBAGS: H₀: The airbags are up to industry standards 3) MR. MAGIC MALE ENHANCER (includes a drug, not approved by the FDA for male Erectile Dysfunction (ED). The drug may interact with Nitrates in prescription medications for heart conditions, high blood pressure, and diabetes, lowering blood pressure to dangerous levels) H₀: This drug has no side effects on blood pressure. (Rogers) (U.S Food and Drug Administration)

 The probability of a Type I Error (α) is the level of significance. (Richardson) α Type I Error α Type II Error

 Power = the probability of rejecting a false hypothesis.  β is the probability of a Type II Error.  To find Power use 1-β.  We want the power of a test to approach 1 (means less likelihood of a Type II Error) (Black 1999)

 Counter-intuitive formulation and generally confusing terminology  A logical claim, not an empirical one  The larger the sample size, the greater the chance of finding a statistically significant difference, regardless of whether the difference is notable  Statistical significance does not tell you anything about the size of the effect being measured

 Statistical significance does not equal importance  Conversely, statistical insignificance does not equal unimportance  “Absence of evidence is not evidence of absence”

 Ronald Carver's 4 suggestions: ◦ Insist that "statistically" be inserted in front of "significant" in research reports. ◦ Insist that the results always be interpreted with respect to the data first, and statistical significance, second. ◦ Insist that attention be paid to the size of the effect, whether it is statistically significant or not. ◦ Insist that new journal editors present their views on statistical significance testing prior to their selection. (Carver 1993)

 Focus instead on estimates of effect size and sampling error  Repeat studies!!!

 Resources  Davis Nachmias. Research Methods in the Social Sciences, Fourth Edition, (New York, 1992),  Wikipedia. “Hypothesis Testing: Origins.” Available at Accessed November 1,  DMAIC Tools: Six Sigma Training Resources. “Hypothesis Testing: Analyze Overview.” Available at Accessed November 1,  Thomas R. Black. "Simulations for Complex Concepts: Teaching Statistical Power as an Example." International Journal of Mathematical Education in Science and Technology 30, no. 4 (1999): Available at dx.doi.org/ / Accessed November 23,  John V. Richardson. Hypothesis Testing: Role of Type I and Type II Errors, Level of Significance (alpha) and Power (Beta). Class Handout. Distributed in IS 280 on November 18, 2010  Tom Rogers. "Type I and Type II Errors." Intuitor: How to Succeed through Creative Learning. Available at Accessed November 23,  U.S. Food and Drug Administration. "Mr. Magic Male Enhancer: Undeclared Drug Ingredient." FDA: Safety. August 18, Accessed November 23, /ucm htm.  Ronald P. Carver “The Case against Statistical Significance Testing, Revisited.” The Journal of Experimental Education, Vol. 61, No. 4, Statistical Significance Testing in Contemporary Practice (Summer, 1993), pp  Bruce Thompson “The Concept of Statistical Significance Testing.” ERIC Clearinghouse on Assessment and Evaluation. Available at Accessed on November 21,  James P. Shaver "Change and Nonsense: A Conversation about Interpreting Tests of Statistical Significance.” The Phi Delta Kappan, Vol. 67, No. 1 (Sep., 1985), pp