PSY302-300310560
From PsychWiki - A Collaborative Psychology Wiki
TESTS
Two-sample t-test: between (independent)
Definition: Testing the relationship between a categorical independent variable and a continuous independent variable, in which the categorical independent variable is a between-subjects design with two levels.
Example:http://news.yahoo.com/s/hsn/20100219/hl_hsn/fdaapproveddiabetesdrugdespitehintsatcancerris
Application:Resaerchers studied the FDA approved diabetes medication Victoza. People are questioning the the approval of the drug based on findings in rats that developed a rare thyroid cancer.Researchers administered the drug to one group of rats and another group served as the control(did not recieve the drug)."The cancer finding in treated rats, compared with the untreated group, was not considered significantly different, statistically, except among male rats that received an eight-fold higher drug exposure than what humans would receive at even the maximum proposed dose."
Two-sample t-test: within (related)
Definition: Testing the relationship between a categorical independent variable and a continuous independent variable, in which the categorical independent variable is a within-subjects design with two levels.
Example:http://www.prepme.com/about/scoreIncreaseReport
Application:"We randomly selected 200 students who enrolled in the PrepMe SAT Platinum program. These students were not restricted to students who had completed the course. We then called these 200 students and each student self reported his or her SAT scores after the PrepMe program[...] We then calculated each student's score improvements from both the initial Diagnostic test to the actual SAT score, and from each student's first practice test to his or her actual SAT score. Both sets of data are shown below as distributions. It is important to note that the average scores on the Diagnostic test are in line with national averages for each section (roughly 520-540 for each section)" In this case the test score before and after are the categorical Independent variables.
One-Way ANOVA test
Definition: Testing the relationship between a categorical independent variable and a continuous independent variable, in which the categorical independent variable is a between-subjects design with three or more levels.
Application:"The abolition of in-feed antibiotics or chemotherapeutics as growth promoters have stimulated the swine industry to look for alternatives such as organic acids, botanicals, probiotics and tannin. The objective of the present study was to compare the effects of a combination of acids and tannin with diet with organic acids and diet without growth promoters on the growth performance and selected biochemical, haematological and antioxidant enzyme parameters in grower pigs[...]Methods: Thirty-six 7 week old grower pigs, divided into three equal groups, were used in a three week feeding trial. Group I was fed basal diet, group II basal diet with added organic acids and group III basal diet with added organic and inorganic acids and tannin." A One-way ANOVA was used to assess any diet related changes of all the parameters.
Two-Way ANOVA test
Definition: Testing the relationship between two categorical independent variable and a continuous independent variable.
Application:"The aim of this investigation was to determine the intra-tester reliability of measuring the thoracic kyphosis angle using a clinical method" The researchers used a two way anova to test to test the intra-tester reliablity. The independent variables being tested were 45 subjects with and without upper body for Factor A and the clinical method of measurement for Factor B. The measurement of the thoracic kyphosis as used in this investigation was found to have excellent intra-rater reliability for both subjects with and without symptoms. The ICC(single) results for the subjects without symptoms were, .95; (95% CI .91-.97).
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Methods: Measurements were made in 45 subjects with and 45 subjects without upper body symptoms. Measurements were made with the subjects in relaxed standing.
Correlation test
Definition: Testing the relationship between two continuous variables, either of which can be considered the independent or dependent variable.
Application: The study refers to the internalization of society's homophobic attitudes within a lesbian, gay, or bisexual (LGB) person. Over the years, researchers have found internalized homophobia to correlate with a variety of psychological, behavioral, and medical outcomes like depression, substance use, and sexual behaviors that put one at risk for HIV and other sexually transmitted infections. Here, the researchers used a meta-analysis to see the relationship between internalization of society's homophobic attitudes within the (LGB).The meta-analysis included 16 studies representing research on nearly 3,000 men.The researchers found a very small relationship between internalized homophobia and sexual risk taking (correlation = .10, p = .053). Most interestingly, they found that the correlation got significantly smaller over time (correlation dropped .02 for every year since 1988) to the extent it is likely to be negligible today.They suggest that negative attitudes towards being gay/bisexual were more important in terms of sexual orientation in the late 1980s and early 1990s, a time when HIV/AIDS was less treatable, carried more stigma, and was more linked to the gay community than it is today.
Chi-square test
Definition: Testing the relationship between two categorical variables, either of which can be considered the independent or dependent variable.
Application: To determine whether 3-hydroxy-3-methylglutaryl coenzyme A reductase inhibitors (statins) and nonsteroidal anti-inflammatory drugs (NSAIDs) are associated with the risk of prostate cancer and improved survival in men with prostate cancer." They examined, "the association between NSAID and statin use among 7042 men who underwent radical prostatectomy (RP, 4611) or radiotherapy (RT, 2431) for prostate cancer between 1990 and 2003 identified in the Cancer of the Prostate Strategic Urologic Research Endeavor (CaPSURE), a primarily community-based national prostate cancer registry. We compared clinical and sociodemographic variables by statin and NSAID use, using chi-square tests and multinomial logistic regression. We examined associations between medications and comorbid illness with mortality using unadjusted and adjusted Cox proportional hazard models. The median (range) follow-up from treatment was 4 (0-16) years." The results are as follows, " In multivariate survival analysis, statin 'ever-use' was associated with a reduced risk of all-cause mortality (ACM) after RP (hazard ratio, HR, 0.35, 95% confidence interval, CI, 0.21-0.58) and RT (0.59, 0.37-0.94). NSAID ever-use was also associated with a reduced risk of ACM after RP (HR 0.47, 95% CI 0.30-0.75) and RT (0.39, 0.25-0.59)."
Concepts
Standard Score
Definition:A score obtained by using the transformation Z=(X-Xbar)divided by S
Example:http://www.businessweek.com/lifestyle/content/healthday/634967.html
Application: The study followed 767 people from a larger study and found that the stress of caring for disabled spouses increased the likelihood of a stroke. The risk seems to be greater in husbands than in wives. The researchers assessed strain using the standard score by aking participants how many days in the last week they felt depressed, lonely, sad, or had crying spells.. Their responses were matched to the Framingham Stroke Risk Score. This assesses risk factors such as age, blood pressure, blood cholesterol levels, smoking and diabetes. A high score on the measure of strain was associated with an overall 23% higher risk of stroke. The association was stronger in husbands than in wives. The risk was highest in black men with high caregiving strain.They have 26.9% increased risk of stroke in the next 10 years.
Confidence Interval
Definition:A range of score values expected to contain the value mu with a certain level of confidence.
Example:http://www.nhs.uk/news/2010/02February/Pages/aspirin-breast-cancer-link-explored.aspx
Application:"This news story is based on research that looked at aspirin use in over 4,000 nurses who had been treated for breast cancer. The study found that there was an association between frequent use of aspirin and a decreased risk of recurrence of cancer and breast cancer-related death.[...]Aspirin was associated with a lower risk of death from breast cancer. For women who took aspirin two to five days a week, there was a 71% lower risk of death (relative risk [RR] 0.29, 95% confidence interval (CI) 0.16 to 0.52) compared to individuals who had never taken aspirin. For women who currently took it between six and seven days a week, risk was 64% lower (RR 0.36, 95% CI, 0.24 to 0.54."
Parametric Test
Definition:A statistical test involving hypotheses that state a relationship about a population parameter
Example: http://www.industryweek.com/articles/a_360_degree_view_of_risk_20786.aspx?SectionID=2
Application: The author of the article first discusses the bad state of the economy and explains why it is imoprtant for companies to assess potential sources of risk.He suggests the z test as a method for doing this. The z test is a sufficent test to use for the company's to predict the likelihood of going bankrupt within two years.The z score calculates several ratio's including, Capital/Total Assets,Retained Earnings/Total Assets, and EBIT/Total Assertions. These ratios show performance measurement in terms of internal parameters like the level of liquid assets, profitability and operating efficiency.
Nonparametric Test
Definition:A statistical test involving hypotheses that do not state a relationship about a population parameter. Also known as a distribution free test.
Application:To determine whether 3-hydroxy-3-methylglutaryl coenzyme A reductase inhibitors (statins) and nonsteroidal anti-inflammatory drugs (NSAIDs) are associated with the risk of prostate cancer and improved survival in men with prostate cancer." They examined, "the association between NSAID and statin use among 7042 men who underwent radical prostatectomy (RP, 4611) or radiotherapy (RT, 2431) for prostate cancer between 1990 and 2003 identified in the Cancer of the Prostate Strategic Urologic Research Endeavor (CaPSURE), a primarily community-based national prostate cancer registry. We compared clinical and sociodemographic variables by statin and NSAID use, using chi-square tests and multinomial logistic regression. We examined associations between medications and comorbid illness with mortality using unadjusted and adjusted Cox proportional hazard models.
The median (range) follow-up from treatment was 4 (0-16) years." The results are as follows, " In multivariate survival analysis, statin 'ever-use' was associated with a reduced risk of all-cause mortality (ACM) after RP (hazard ratio, HR, 0.35, 95% confidence interval, CI, 0.21-0.58) and RT (0.59, 0.37-0.94). NSAID ever-use was also associated with a reduced risk of ACM after RP (HR 0.47, 95% CI 0.30-0.75) and RT (0.39, 0.25-0.59)." Here, there is no relationship stated about a population parameter therefore, it is a nonparametric test.
Statistically significant difference
Definition: The observed value of the test statistic falls into the rejection region and HO is rejected.
Example: http://money.cnn.com/news/newsfeeds/articles/marketwire/0583516.htm
Application: In a recently completed clinical study at the University of Western Australia, the reseachers found that the rate of influenza-like illnesses was significantly (p=0.01) reduced from 71% to 43% in interferon treated subjects who recieved Fluvax, which is an influenza vaccine.Therefore,it was significantly different and the drug did help flu symptoms.
Nonsignificant difference
Definition:The observed value of the test statistic does not fall into rejection region and the null hypothesis is not rejected.
Example:http://www.hemonctoday.com/article.aspx?rid=61125
Application:"The use of estrogen plus progestin hormone therapy increased risk for lung cancer in perimenopausal and postmenopausal women by about 25% when used for one to nine years and by about 50% when used for 10 years or more[...] Researchers pooled data on 36,588 perimenopausal and postmenopausal women aged 50 to 76 years included in the Vitamins and Lifestyle Study between 2000 and 2002. Mean follow-up was 5.9 years[...] Three hundred and forty-four lung cancer cases were identified: 77% were non–small cell lung cancer cases, 12.5% were small-cell lung cancer cases and 10.5% were other lung cancer cases[...]Women who were current or former users of hormone therapy had a nonsignificant elevated risk for lung cancer."
Between-subjects Design, with two groups
Definition: An experiment in which two or more are created
Example:http://www.hptn.org/research_studies/hptn052.asp
Application: Here, is a research design about HIV prevention with two different groups. "Based on data collected in Africa and Thailand, there is a correlation between HIV viral load (blood levels) and HIV transmission. Specifically, the higher the viral load in the blood, the more likely the chance for transmission. Antiretroviral therapy (ART) reduces the viral load in the blood, as well as in genital secretions (for both men and women), and the drugs can be detected in semen and vaginal and cervical secretions. All of this information strongly suggests that ART may make HIV-infected people less contagious. HPTN 052 compares the HIV‑infection rates of two groups of HIV-serodiscordant couples. The index case of the first group starts taking ART as soon as the couple is enrolled in the study, while the index case of the second group starts taking ART when he or she has two consecutive measurements of a CD4+ cell count within or below the range of 200-250 cells/mm3, or when he or she develops an AIDS-defining illness"
Between-subjects Design, with three or more groups
Definition:An experiment in which three or more groups are created
Example:http://bjp.rcpsych.org/cgi/content/abstract/196/3/200
Application: The study was Cognitive style, persoanlity, and vulnerablity to postnatal depression on. The authors stated: "Only some women with recurrent major depressive disorder experience postnatal episodes. Personality and/or cognitive styles might increase the likelihood of experiencing postnatal depression." The aim of the study was to establish whether personality and cognitive style predicts vulnerability to postnatal episodes over and above their known relationship to depression in general. The authors used a between-subjects design, with three groups. They compared, "personality and cognitive style in women with recurrent major depressive disorder who had experienced one or more postnatal episodes (postnatal depression (PND) group, n=143) with healthy female controls (control group, n=173). We also examined parous women with recurrent major depressive disorder who experienced no perinatal episodes (non-postnatal depression (NPND) group, n=131).
Random sampling
Definition: A sample in which indivduals are selected so that each member of the popuation has an equal chance of being selected for the sample, and the selection of one member is independent of the selection of any other member of the population.
Example:http://www.cbsnews.com/blogs/2010/02/11/politics/politicalhotsheet/entry6198284.shtml
Application:A study showing Americans support for homosexuals in the military depends on the way the question is asked.Different results were discovered when the question was asked the exact why in the previous sentence compared to asking if "Americans support gay men and lesbians in the military"."This poll was conducted among a random sample of 1,084 adults nationwide, interviewed by telephone February 5-10, 2010. Phone numbers were dialed from random digit dial samples of both standard land-line and cell phones. The error due to sampling for results based on the entire sample could be plus or minus three percentage points. The error for subgroups is higher." In this study,each member of the population had an equal chance of being selected for the sample, and the selection of one member was independent of the selection of another member from the population.
Random Assignment
Definition:A method of assigning subjects to treatment groups so that an indivdual selected for the experiment has an equal probability of assignment to any of the groups and the assignment of one subject to a group does not affect the assignment of any other indivdual to that same group.
Example: http://multivu.prnewswire.com/mnr/alli/41873/
Application:"In the six-month Visceral Fat Multi-Center Study, overweight and obese adults receiving alli while on a reduced calorie, lower-fat diet had significantly greater improvements in visceral fat than those treated with diet alone.In this study, 123 participants were randomly assigned to receive either alli three times per day or a placebo, along with recommendations to follow a reduced calorie, lower-fat diet, for 24 weeks. At week 24, statistically significant reductions in visceral fat and body weight were observed in both groups; however, the reduction was significantly higher among patients taking alli. Mean reductions in visceral fat were 15.66 percent for alli versus 9.39 percent for placebo (P<0.0001); mean reductions in body weight were 5.96 kg versus 3.91 kg, respectively (P<0.05).2." In this study, the subjects were randomly assigned because each subject had an equal probability of being assigned to either group and the assignment of one indivdual did not affect the assignment of another indivdual to that same group.
Independent Variable
Definition: A variable manipulated in an experiment to determine its effect on the dependent variable.
Application: "The aims of this study were to estimate the prevalence of left ventricular systolic (LVSD) and diastolic (LVDD) dysfunction, and to test if BNP(Brain natriuretic peptide) and urinary albumin excretion rate (AER) are related to LVSD, LVDD and left ventricular mass (LVM) in asymptomatic type 2 diabetes patients[...] LVSD was present in 6.1% of patients whereas 49% (29% mild, 19% moderate and 0.7% severe) had LVDD and 9.4% had left ventricular hypertrophy. Increasing age (P<0.0001) was the only independent variable related to mild LVDD whereas increasing BNP (P=0.01), systolic blood pressure (P=0.01), age (P=0.003) and female gender (P=0.04) were independent determinants of moderate to severe LVDD."
Levels of the Independent Variable
Definition:One value of the indepedent variable. To be a variable, an indepedent variable must take on at least two levels.
Example:http://www.gallup.com/poll/126065/Makes-700-Million-Adults-Migrate.aspx
Application: "Gallup analyzed people's desires to migrate using several independent variables such as sex, age, education, confidence in national leadership, local institutions, corruption in business and government, the presence of transnational social networks, and others." Here, their are 8 levels of the independent variable
Confounds
Definition: An extraneous variable that is covarying with the independent variable, potentially masking the true effects of the independent variable on the dependent variable
Example:http://www.aidsmeds.com/articles/abacavir_cardiovascular_denmark_1667_17965.shtml
Application: One study found that the HIV medicine, Abacavir increased the risk of heart attack by 95% This risk remians high even after the drug is stopped. More recently, the risk of heart attack associated with the medication has gone down to 70%. This is most likely due to recent data regarding confounding variables such as cholesterol and triglyceride levels.
Dependent Variable
Definition:The variable in an experiment that depends on the independent variable. In most instances the dependent variable is some measure of a behavior. Note: this is not the case for the following example.
Example:http://www.medscape.com/viewarticle/717704
Application: The article discusses the likelihood of a Vitamin D deficency among patients starting dialysis. "Using logistic regression modeling, neural networks, and decision trees with vitamin D deficiency as the dependent variable, the investigators generated predictive models from routinely determined clinical and demographic data in the training set. To identify the simplest model that remained predictive, the investigators subjected the models to progressive variable reduction."
Within-subjects Design, with two groups
Definition: A research design in which one group of subjects is exposed to and measured under each level of an independent variable. In a with-subjects designs, each subject recieves each treatment condition.
Example:http://www.prepme.com/about/scoreIncreaseReport
Application:"We randomly selected 200 students who enrolled in the PrepMe SAT Platinum program. These students were not restricted to students who had completed the course. We then called these 200 students and each student self reported his or her SAT scores after the PrepMe program[...] We then calculated each student's score improvements from both the initial Diagnostic test to the actual SAT score, and from each student's first practice test to his or her actual SAT score. Both sets of data are shown below as distributions. It is important to note that the average scores on the Diagnostic test are in line with national averages for each section (roughly 520-540 for each section)"
Within-subjects Design, with three or more groups
Definition:A research design in which one group of subjects is exposed to and measured under each level of an independent variable. In a with-subjects designs, each subject recieves each treatment condition.
Example:stats class
Application:So I looked and looked and good not find an example, but I know it's the same subject exposed to three different levels of an independent variable. For example if one were trying to test the effects of a test strategy and they exposed the subjects to three different levels of that independent variable.
Main effect
Definition: The mean of all subjects given one level of the indepedent variable, ignoring the classification by the other independent variable in a factorial design.
Example:http://www.docguide.com/news/content.nsf/news/852576140048867C852576D90068628F
Application: "Varenicline may acutely decrease smokers' enjoyment of smoking, but not smoking reinforcement, according to a study presented here at the 2010 Society for Research on Nicotine and Tobacco (SRNT) Annual Meeting[...]Dr. Perkins and colleagues conducted a study to examine the effects of varenicline versus placebo on smoking behaviour and reward during a single acute smoking session[...]A repeated measures analysis of variance showed a main effect of varenicline on liking (P < .001), similarity to their own brand (P < .001), and how much nicotine (P < .05). There were no effects of varenicline on smoking behaviour."
Interaction
Definition:A situation in a factorial design in which both effect of one indepedent variable depends on the level of the other indepedent variable with which this combined.
Example:http://www.physorg.com/news187618310.html
Application: This study tested the effects of people who followed carbohydrate diet versus people who followed a low fat diet. They also studied the effect of visits to the peron overseeing the subjects diet plan with the dietary assignment of subjects "The difference in weight loss between groups was not significant between the diet groups at 36 months (P = 0.071 before and P = 0.056 for the interaction between visit and dietary assignment after adjustment for baseline variables). Here, the interaction between visit and dietary assignment was not significant. This means that the effect of one independent variable did not make a difference when coupled with a level of the other independent variable.
Strength of Effect (Eta squared)
Definition:The strength of the effect shows how closely related to variables are to one another. It shows how strong a significant finding is
Example:http://www.annals.org/content/119/7_Part_1/599.abstract
Application: The purpos was: "To assess the size and consistency of garlic's effect on total serum cholesterol in persons with cholesterol levels greater than 5.17 mmol/L (200 mg/dL)[...] Clinical trials were identified by a computerized literature search of MEDLINE and by an assessment of the bibliographies of published studies and reviews[...] Trials were selected if they were randomized and placebo-controlled and if at least 75% of their patients had cholesterol levels greater than 5.17 mmol/L (200 mg/dL). Studies were excluded if they did not provide enough data to compute effect size. Five of 28 studies were selected for review." Basically to test tbe effect of garllic on total serum cholesterol, the researchers used various studies that were already conducted.One of the criteria's for selecting a study was based on whether an effect size also, referred to as eta squared had been computed. The effect size or eta squared would show how strong the effect of garlic was on serum cholesterol in a person.
Scatterplot
Definition: A plot of a bivariate distribution in which the X variable is plotted on the horizontal axis and the Y variable is plotted on the vertical axis.
Example:http://www.theatlantic.com/national/archive/2010/02/what-makes-cities-happy/36120/
Application: The data show two variables, well being and income, so the plot is bivariate, and represents income on the X axis, and well being on the Y axis, resulting in a scatterplot.
Positive relationship
Definition:A relationship between two variables in which, as the value of one of the variables increases, the value of the other variable tends to increase also.
Application: The article discusses income tax marginal rate. "When filing your 2009 taxes, you may be interested in the Income tax marginal rate. The marginal rate tax rate is the taxes that you would pay on an additional dollar of income. In the United States, the marginal tax rate has a positive correlation with the amount of money that you earn. As your income increases, the percentage of taxes that you will owe also increases."
Negative relationship
Definition: A relationship between variables in which, as the value of one variable increases, the value of the other variable tends to decrease.
Example:http://www.hamilton.edu/spectator/021810/news/health.html
Application: An Economics Professor, Jonathan Skinner, discusses health care reform in the United States. "He laid out facts and figures about health care, and he evaluated the possible reasons why Americans need health care reform. Skinner concluded by proposing his own solution, a comprehensive overhaul to the current system.[...] Skinner works with the Dartmouth Atlas of Health Care, which examines how health care practices and costs differ across different regions of the country. Skinner presented one map, for example, that showed the Miami-Dade area having the highest individual costs. The rest of the map revealed the drastic variations in health care costs across the country.Skinner said that more spending does not buy better quality health care; in fact, there was a negative correlation between cost and quality of care."
No relationship
Definition: Term used in a correlational study when the two variables being compared share no relationship to one another.
Application: The article measures personal income patterns and profiles for South Africa in 2009."Carel van Aardt and Marietjie Coetzee show in their report on personal income in South Africa during 2009 (BMR Report 387) that negative GDP and employment growth during 2009 had a direct impact on personal income growth and the distribution of such income growth." They found many positive and negative correlates collapsed among various situations, but interestingly to them, found no correlation between income and part-time employment since the majoority of part-time jobs are not high-paying.
Linear relationship
Definition:A relationship between two variables that can be described by a straightline.
Example:http://www.theatlantic.com/national/archive/2010/02/what-makes-cities-happy/36120/
Application:The article, "What Makes Cities Happy," discusses some of the social, demographic, and economic factors that might be associated with the happiness and well-being of cities."The Gallup-Healthways is the first comprehensive data set we know of that tracks happiness and well-being at the metropolitan level, providing data from a large-scale survey of individuals across 185 metro regions. We look at the associations between the Gallup-Healthways Metro happiness index and key social, demographic, and economic factors--like income, unemployment, high-technology industry, and socioeconomic structure. Data-matching reduces the size of our sample to 170 metros--roughly half of all U.S. regions." Income, Wages, and Output: "So what is the relationship between metro-level happiness and income, wages, and output? We find moderate correlations between city happiness and wages (.45), income (.4), and economic output per capita (.37). The scatter-graphs below show the relationships are reasonably linear, though there is a better fit for wages and income than for output per capita." Therfore,a straightline can be used to describe the relationship between between wages and city happiness.
Curvilinear relationship
Definition: A relationship between two or more variables which is depicted graphically by anything other than a straight line
Example:http://www.cherwell.org/content/9998
Application:The article "Beer before wine, a scientifically -sound rhyme?," discusses most westernized cultures sayings, "Beer before wine, wine before beer- oh deer," versuses the contadictory American saying, "beer before liquor, never be sicker." One defender of the american saying says that it is easier on your body to absorb weaker alcholic drinks, like beer, later on in the evening. While there have been few studies on this the author found a very old study and a more recent study to test this theory: " One study that took place back in the golden ages of prohibition found that low alcohol concentrations (2.75%) were absorbed at a slower rate than higher concentrations (27.5%). A later set of experiments testing out a wider range of concentrations however argued for a ‘curvilinear’ relationship. Here, scientists found that alcohol drunk at concentrations more closely resembling those of wine (15%) or neat spirits (45%) were absorbed more slowly than a mid-range concentration of 30%."
Coefficient of Determination
Definition:The value r2 indicating the common variance of variables X and Y.
Example:http://www.hotelnewsnow.com/articles.aspx?ArticleId=2792&PageType=News&ArticleType=35
Application:The article, "Adding weight to your competitive set," suggest a new tool for hotels to use to specifically determine their competition. "The new tool developed by STR Analytics is the Market-Weighted Penetration Index Analysis, which uses a multiple regression model to objectively determine what competitors are most statistically significant to your hotel and then readjusts your penetration index accordingly. Multiple regression is a flexible, statistical process of analyzing several variables, namely a dependent variable (i.e. your property's daily RevPAR) to any other independent variables (i.e. competitors' daily RevPAR). In simple terms, the primary indicating factor in the regression analysis is R2.R2 = Coefficient of determination. R2 represents the proportion of the variance in one variable that is explained by the other variables. In other words, R2 represents how well your property’s RevPAR variations are For example: If R2 is 0.85 that indicates that 85 percent of the total variation in your hotel's RevPAR can be explained by the relationship between your hotel and its competitive set. Strong relationships indicate high levels of competition within a competitive market. Assuming your competitive set is the most appropriate to benchmark your performance (which may have changed in the new economy and is worth examining) then the R2 should be significant."
Correlation does not equal causation
Definition:Variables can be highly correlated, but the existence of a correlation between variables x and y does not imply one causes the other.
Application: The article is about the correlation of the measles shot to autism. One man's research suggested that the MMR caused an unknown bowel disorder which somehow triggered Autism. Many parents in turn were afraid have their child get this shot which caused a surge in measles outbreaks in 2006. Scientists recieved this correlation with caution.Even back then it was received with caution. "They warned that such a radical claim based on such slim evidence (a bare dozen cases) needed much more testing and corroboration before the MMR jab - which saves thousands of lives - was abandoned. Wakefield himself only suggested separating out the three jabs, not getting rid of them altogether." Scientits are now saying that this correlation was only found because autism 'presents' naturally at around the same age that children get their vaccine jabs. "As any logician will tell you, Correlation Does Not Imply Causation."
Extra-Credit (3 points each)
Normal Distribution
Definition:A theoretical mathematical distribuion that specifies the relative frequency of a set of scores in a population
Example:http://kermittheblog.wordpress.com/2007/05/10/beisbol-been-barry-barry-good-to-uh-barry/
Application:The article is about the baseball player Barry Bonds and his successful performance and overwhelming amount of home runs. The article uses a normal distribution to desribe his performance which places him two standard deviations above the mean therefore, making him an outlier. The performaces in the population of professional baseball are normally distributed. It shows the relative frequency of scores in baseball performance.
Symmetrical
Definition:A frequency distribution that when folded at a midpoint produces two halves identical in shape.
Example:http://kermittheblog.wordpress.com/2007/05/10/beisbol-been-barry-barry-good-to-uh-barry/
Application:The article is about the baseball player Barry Bonds and his successful performance and overwhelming amount of home runs. The article uses a normal distribution to desribe his performance which places him two standard deviations above the mean therefore, making him an outlier. This normal distribution is symmetrical. If you folded it at a midpoint, the two halves would be identical in shape.
Asymptotic
Define: A distribution for which the tails of the distribution never touch the x axis
Example:http://kermittheblog.wordpress.com/2007/05/10/beisbol-been-barry-barry-good-to-uh-barry/
Application:The article is about the baseball player Barry Bonds and his successful performance and overwhelming amount of home runs. The article uses a normal distribution to desribe his performance which places him two standard deviations above the mean therefore, making him an outlier. This normal distribution is asymptotic. The tails in this normal distribution never touch the x axis.
Continuous
Definition:A distribution for which, if any two scores in the distribution are chosen, another score that lies between them can always be found.
Example:http://kermittheblog.wordpress.com/2007/05/10/beisbol-been-barry-barry-good-to-uh-barry/
Application:The article is about the baseball player Barry Bonds and his successful performance and overwhelming amount of home runs. The article uses a normal distribution to desribe his performance which places him two standard deviations above the mean therefore, making him an outlier. This normal distribution is a continuous distribution in which the scores range from negative infinity in one tail to positive infinity in the other tail. Another score that lies between these two tails can always be found.
Sampling Error
Definition: The amount by which a sample mean differs from the population mean
Example:http://www.gallup.com/poll/126338/Obama-Retains-Trust-Congress-Healthcare.aspx
Application: The article compares Americans confidence in healthcare reform recommendations from Obama,Demoocratic leaders in Congress, and Repulblican leaders in Congress. As it stands now, " Americans remain more confident in the healthcare reform recommendations of President Obama (49%) than in the recommendations of the Democratic (37%) or Republican (32%) leaders in Congress. But these confidence levels are lower than those measured in June, suggesting that the ongoing healthcare reform debate has taken a toll on the credibility of the politicians involved." The Gallup reports from June revealed that "Obama elicited higher confidence (83%) than Democrats in Congress (67%) do from rank-and-file Democrats as well as from independents (44% vs. 30%), helping explain why Obama's overall confidence ratings are higher than the Democrats'. Republicans in Congress get a 64% confidence rating from Republicans. Independents are less positive about either party's leaders in Congress than they are about Obama.Results are based on telephone interviews with a random sample of 992 national adults, aged 18 and older, conducted March 2-3, 2010, as part of Gallup Daily tracking. For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±4 percentage points.
Null Hypothesis
Definition:A statement of condition that a scientist tentatively holds to be true about a population. The null hypothesis is the hypothesis tested by a statistical test.
Example:http://ang.sagepub.com/cgi/content/abstract/47/2/139
The article,"Critism of Cardiovascular Studies with Negative Results Due to a Negative Correlation, critisizes cardiovascular studies that have been published regarding negative results due to negative relatioships. The author states "Trials that do not allow rejection of the null hypothesis of no treatment effect may have had an inappropriate design. Self-controlled trials, although routinely used for the study of cardiovascular diseases, are virtually never assessed for correlation between treatment modalities." The implication of a "null hypothesis" is that there is no difference at the population level. Thus, in this case, the "null hypothesis of no treatment effect" means that the treatment will have no effect if measured at the population level.
Alternative Hypothesis
Significance level
Definition: A probablity value that provides the criterion for rejecting the null hypthesis in a statistical test.
Application:"a biopharmaceutical company focused on the development of therapeutics to treat cancer and hepatitis, today announced that the primary endpoint of improvement in overall survival was not met in Novelos' pivotal Phase 3 trial in advanced non-small cell lung cancer (NSCLC) studying its lead product, NOV-002, in combination with first-line chemotherapy[...]This randomized, controlled, open-label Phase 3 trial, conducted under a Special Protocol Assessment (SPA) and Fast Track designation, had enrolled 903 patients with Stage IIIb/IV NSCLC, which includes all histological subtypes. The trial, conducted across approximately 100 clinical sites in 12 countries, evaluated NOV-002 in combination with first-line paclitaxel and carboplatin chemotherapy versus paclitaxel and carboplatin alone. The primary efficacy endpoint of the trial was improvement in overall survival. Enrollment commenced in November 2006, target enrollment was achieved in March 2008, and the 725 event (patient death) was announced in early January 2010. According to the trial's Statistical Analysis Plan (SAP), a total of 725 events were required to detect a 25% improvement (12.5 months versus 10 months) in overall median survival (hazard ratio of 0.8) with 85% power and a two-sided significance level of 0.05. No interim analysis was performed." At the significance level of 0.05, the phase 3 trial value did not fall into rejected and was therefore found to be statistically not significant."
Two-tailed test
Definition:A statistical test using rejection regions in both tails of the sampling distribution of the test statistic. Also called nondirectional.
Application::"a biopharmaceutical company focused on the development of therapeutics to treat cancer and hepatitis, today announced that the primary endpoint of improvement in overall survival was not met in Novelos' pivotal Phase 3 trial in advanced non-small cell lung cancer (NSCLC) studying its lead product, NOV-002, in combination with first-line chemotherapy[...]This randomized, controlled, open-label Phase 3 trial, conducted under a Special Protocol Assessment (SPA) and Fast Track designation, had enrolled 903 patients with Stage IIIb/IV NSCLC, which includes all histological subtypes. The trial, conducted across approximately 100 clinical sites in 12 countries, evaluated NOV-002 in combination with first-line paclitaxel and carboplatin chemotherapy versus paclitaxel and carboplatin alone. The primary efficacy endpoint of the trial was improvement in overall survival. Enrollment commenced in November 2006, target enrollment was achieved in March 2008, and the 725 event (patient death) was announced in early January 2010. According to the trial's Statistical Analysis Plan (SAP), a total of 725 events were required to detect a 25% improvement (12.5 months versus 10 months) in overall median survival (hazard ratio of 0.8) with 85% power and a two-sided significance level of 0.05. No interim analysis was performed." At the significance level of 0.05, the phase 3 trial value did not fall into rejected and was therefore found to be statistically not significant." In other words, the researchers used a two-tailed test to test the validity of the phase 3 trial of the drug.
One-tailed test
Definition:A statistical test employing a rejection region in only one tail of the sampling distribution of the test statistic. Example:http://bjp.rcpsych.org/cgi/content/abstract/196/3/173
Application:"To examine indicators of publication bias in randomized controlled trials of psychotherapy for adult depression." They examined effect sizes of 117 trials with 175 comparisons between psychotherapy and control conditions. As indicators of publication bias they examined funnel plots, calculated adjusted effect sizes after publication had been taken into account using Duval & Tweedie’s procedure, and tested the symmetry of the funnel plots using the Begg & Mazumdar rank correlation test and Egger’s test."The mean effect size was 0.67, which was reduced after adjustment for publication bias to 0.42 (51 imputed studies). Both Begg & Mazumbar’s test and Egger’s test were highly significant (P<0.001)." Here, they used a one tailed test to examine indicators of publication bias in randomized controlled trials of psychotherapy for adult depreesion. This means that the stat test for this used only one tail for it's rejection region.
Degrees of Freedom
Definition:The number of scores free to vary when calculating a statistic.
Example:http://jeb.sagepub.com/cgi/content/abstract/1/1/69
Application:"It has been suggested that when the variance assumptions of a repeated measures ANOVA are not met, the df of the mean square ratio should be adjusted by the sample estimate of the Box correction factor, . This procedure works well when is low, but the estimate is seriously biased when this is not the case. An alternate estimate is proposed which is shown by Monte Carlo methods to be less biased for moderately large." Here, the researcher is saying that when the assumption of their test are not met that the degrees of freedom left to vary need to be adjusted.
Type I Error
Definition:The error in statistical decision making that occurs if the null hypothesis is rejected when it is actually true of the population.
Application: "It is well known that genotyping error adversely affects the power of genetic case-control association studies but there is little research on its effects on type I error, and none that has addressed possible differences in genotype error rates between cases and controls. Methods: We used simulations to examine the influence of genotyping error on the type I error probability given by case-control studies. The effect of genotyping error on the magnitude of type I error was explored for a single marker of varying minor allele frequency (MAF), and for haplotypic tests based on two markers with varying MAF and linkage disequilibrium (LD) measure r 2 . Results: We show that even with low genotyping error rates ( ! 0.01), systematic differences in the error rate between samples can result in type I error rates substantially above 0.05. The effect was maximal for markers with small MAF, markers in strong LD, and where a common allele is more frequently misclassifi ed as a rare allele than vice versa. The problem was also exacerbated by the use of large samples. Conclusions: Our results show that small differential genotyping error rates between cases and controls pose signifi cant problems for association analyses. Differential genotyping error rates are particularly likely to arise where genotype data are combined from multiple sites, or where case genotypes are examined against archived reference population cohort genotypes that are being generated in several countries. Although these strategies may be necessary to obtain adequately powered samples, our data show the importance of stringent quality control. Furthermore, associations based on rare haplotypes should be treated with caution."
Type II Error
Power
Definition: The probablity of rejecting Ho when Ho is false and H1 is true. The power of a statistical test is given by 1-B.
Application::"a biopharmaceutical company focused on the development of therapeutics to treat cancer and hepatitis, today announced that the primary endpoint of improvement in overall survival was not met in Novelos' pivotal Phase 3 trial in advanced non-small cell lung cancer (NSCLC) studying its lead product, NOV-002, in combination with first-line chemotherapy[...]This randomized, controlled, open-label Phase 3 trial, conducted under a Special Protocol Assessment (SPA) and Fast Track designation, had enrolled 903 patients with Stage IIIb/IV NSCLC, which includes all histological subtypes. The trial, conducted across approximately 100 clinical sites in 12 countries, evaluated NOV-002 in combination with first-line paclitaxel and carboplatin chemotherapy versus paclitaxel and carboplatin alone. The primary efficacy endpoint of the trial was improvement in overall survival. Enrollment commenced in November 2006, target enrollment was achieved in March 2008, and the 725 event (patient death) was announced in early January 2010. According to the trial's Statistical Analysis Plan (SAP), a total of 725 events were required to detect a 25% improvement (12.5 months versus 10 months) in overall median survival (hazard ratio of 0.8) with 85% power and a two-sided significance level of 0.05. No interim analysis was performed." At the significance level of 0.05, the phase 3 trial value did not fall into rejected and was therefore found to be statistically not significant." Here, the power of failing to reject Ho was .85 or 85%.
Pairwise comparisons
Definition: Statistical comparisons involving two means.
Application:"The Pairwise compares every team in the country. The system measures four components -- RPI, a team's record against teams under consideration for the tournament (top 25 in RPI), a team's record against common opponents, and head-to-head record[...] According to the Pairwise, Michigan State (17-10-5, 12-7-5-2 Central Collegiate Hockey Association) would be in the NCAA Tournament if the season ended today. Michigan (17-15-1, 12-11-1) is not even among the top 25 teams being considered after getting swept at Nebraska-Omaha over the weekend." The test was "pairwise" because it involved two means - in this case, two teams.
Post-hoc comparisons
Definition: Statistical tests that make all possible pairwise compairsons after a statistically significant Fobs has occured for the overall analysis of variance. Example:http://www.ethiopianreview.com/news/10919
Application:"A team from the VCU Medical Center in Richmond, Virginia, carried out a post-hoc analysis of postmenopausal women <55 or >/=55 years old with low bone mineral density (BMD), randomised to once weekly alendronate 70mg or risedronate 35mg for one year with one-year extensions in US and International Fosamax Actonel Comparison Trials." The results of the post-hoc analysis were as follows: "Changes in BMD were not significantly different between younger and older alendronate-treated women, although treatment differences favoring alendronate were numerically greater for younger than older postmenopausal women at all sites.Significantly greater reductions in bone turnover markers also occurred with alendronate vs risedronate in both subgroups. Tolerability was similar between treatments."
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