PSY302-300967802
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://content.nejm.org/cgi/content/full/NEJMoa1001286
Application: The ACCORD Study Group investigated whether therapy targeting normal systolic pressure reduces major cardiovascular events in participants with type 2 diabetes at high risk for cardiovascular events. Statistical analyses were conducted at the coordinating center with the use of S-Plus software. Baseline characteristics and key safety outcomes were compared between the two study groups with the use of the chi-square test, Fisher's exact test, Wilcoxon rank-sum test, and the two-sample t-test. A total of 4733 participants with type 2 diabetes were randomly assigned to intensive therapy, targeting a systolic pressure of less than 120 mm Hg, or standard therapy, targeting a systolic pressure of less than 140 mm Hg.
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.valdosta.edu/coe/psychology/io/documents/within_subjects_t_test.pdf
Application: A within-subjects t-test was conducted to determine the effect of commercial viewing on attitudes toward an oil company. Using a two-tailed .05 criterion, we fail to reject the null hypothesis. There is no significant difference between attitudes before the commercial and after the commercial.
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: 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. One-way ANOVA was used to assess any diet related changes of all the parameters. Paired t-test was used to evaluate changes of blood parameters individually in each group of growers before and after feeding.
Two-Way ANOVA test
Definition: Testing the relationship between two categorical independent variable and a continuous independent variable.
Application: Clinical sagittal plane assessment of the thoracic kyphosis angle is considered an essential component of the postural examination of patients presenting with upper body pain syndromes. The aim of this investigation was to determine the intra-tester reliability of measuring the thoracic kyphosis angle using a clinical method. Measurements were made in 45 subjects with and 45 subjects without upper body symptoms. Measurements were made with the subjects in relaxed standing. Each set of 3 measurements was made on two occasions (separated by a minimum of 30 minutes and additional data collection involving 46 further measurements of posture and movement on the same and an additional subject before the thoracic kyphosis measurements were re-measured) by one rater. The reliability of the measurements was analyzed using two-way ANOVA test correlation coefficients (ICC), 95% confidence intervals (CI) and standard error of measurement (SEM) for precision, for a single measurement and the average of 3 measures.
Correlation test
Definition: Testing the relationship between two continuous variables, either of which can be considered the independent or dependent variable.
Example: http://www.pustaka-deptan.go.id/publikasi/ja012084.pdf
Application: Leaf analysis can be used as a guide to diagnose nutritional status and as a fertilizer recommendation tool for mangosteen plant. Leaf age is the main important factor to estimate plant nutritional status. The best of leaf sampling is the one which has the best correlation between leaf nutrient concentration with growth and yield. Leaf nutrient concentration was investigated on the mangosteen orchard at Bogor, Tasikmalaya, and Purwakarta, West Java. Twenty relatively uniform and representative mangosteen trees were selected, and every month a leaf sample was analyzed for P concentration. Leaf samples were taken at 2 months after flush and then periodically up to 10 months. Observations were done for number of open flower, number of dropped flower, and number as well as weight of fruit per plant. While for fruit quality, analysis was done on the TSS of the flesh and the N, P, and K content of fruit parts. The results showed that leaves of 4 and 5 month ages were the best to be used as leaf samples to diagnose P status since they have the highest correlation (above 0.7) between P concentration in the leaf and fruit yield. P concentration in the leaves decreased as the age of leaves increased. Mangosteen leaves from Purwakarta contained more P than those from Tasikmalaya and Bogor. This results can be used as a guide to estimate fertilizer recommendations for mangosteen.
Chi-square test
Definition: Testing the relationship between two categorical variables, either of which can be considered the independent or dependent variable.
Example: http://content.nejm.org/cgi/content/full/NEJMoa1001286
Application: Also in the ACCORD Study Group, which investigated whether therapy targeting normal systolic pressure reduces major cardiovascular events in participants with type 2 diabetes at high risk for cardiovascular events. In their statistical analyses, they also used the chi-square test (along with the Fisher's exact test, Wilcoxon rank-sum test, and the two-sample t-test) to fine the baseline characteristics and key safety outcomes were compared between the two study groups. A total of 4733 participants with type 2 diabetes were randomly assigned to intensive therapy, targeting a systolic pressure of less than 120 mm Hg, or standard therapy, targeting a systolic pressure of less than 140 mm Hg.
Concepts
Standard Score
Definition: In statistics, a standard score indicates how many standard deviations an observation or datum is above or below the mean.
Application: The article above shows how they converted raw scores into final scores that are shown in the World’s Best Universities rankings tables. The data was collected and calculated to find the standard scores for each section of data when they are compatible.
Confidence Interval
Definition: A range of score values expected to contain the value of mu with a certain level of confidence.
Example: http://www.jstor.org/pss/170840
Application: The paper above presents a lemma giving the asymptotic properties of a standardized series under quite general conditions. Confidence intervals can be constructed using this lemma. When independent replications of the series are available, such as in computer simulation experiments, these interval estimators may be combined with the classical confidence interval estimator. In an empirical study using three elementary simulated processes, the interval estimators presented here compare favorably with the classical interval estimator.
Parametric Test
Definition: A statistical test involving hypotheses that state a relationship about a population parameter.
Application: Huntington’s disease, a disorder of the basal ganglia, is prevalent in approximately 5-7 per 100,000 people, with an average age of onset of symptoms being at 35-45 years of age. The duration between onset and severe disability or death spans an average of 17 years; most patients die of secondary reasons of the disease such as pneumonia. The fMRI imaging results depicted a statistical parametric map illustrating differences in BOLD response between HD gene carriers and controls during perception of disgusted facial expression.
Nonparametric Test
Definition: A statistical test involving hypotheses that do not state a relationship about a population parameter. Also knows as a distribution-free test.
Example: http://content.nejm.org/cgi/content/full/NEJMoa1001282
Application: As noted in the aforementioned ACCORD Study Group research, nonparametric tests were used in order to measure results (shown in one of their results tables). Shown in the table are the mean plasma levels of total cholesterol (Panel A), low-density lipoprotein (LDL) cholesterol (Panel B), and high-density lipoprotein (HDL) cholesterol (Panel C) and median levels of triglycerides (Panel D) at baseline, 4 months, 8 months, 1 year, and annually thereafter. Nominal P values for differences between the study groups at 4 months and at the end of the study were, respectively: total cholesterol, P<0.001 and P=0.02; LDL cholesterol, P=0.11 and P=0.16; HDL cholesterol, P<0.001 and P=0.01; and triglycerides, P<0.001 for both comparisons with the use of nonparametric tests. End-of-study visits were those that occurred in early 2009 and included follow-up at years 4, 5, 6, and 7. The I bars represent 95% confidence intervals. To convert the values for cholesterol to millimoles per liter, multiply by 0.02586. To convert the values for triglycerides to millimoles per liter, multiply by 0.01129.
Statistically significant difference
Definition: The observed value of the test statistic falls into a rejection region H0 is rejected.
Example: http://online.wsj.com/article/BT-CO-20100314-702798.html?mod=WSJ_latest-headlines
Application: A new study found that Novartis AG's blockbuster blood-pressure drug Diovan modestly lowered the incidence of diabetes in certain high-risk patients, but another Novartis drug failed to do so. Neither drug reduced the risk of heart attacks and related disease in these patients. Some 36% of Starlix users developed diabetes, versus 34% in the placebo group. There was statistically significant difference in rates of cardiovascular events between Starlix and placebo. Also, Starlix increased the risk of high blood sugar.
Nonsignificant difference
Definition: The observed value of a test statistic does not fall into a rejection region in the null hypothesis is not rejected.
Example: http://www.medscape.com/viewarticle/718401
Application: Top-line results of 2 phase 3 trials of latrepirdine (Dimebon, Medivation/Pfizer) show that the drug failed to meet either primary or secondary endpoints versus placebo for the treatment of Alzheimer's disease (AD). The results have caused not only disappointment but some skepticism about the original phase 2 results with latrepirdine, published in the Lancet in 2008, which had shown extremely positive response to the drug. After 6 months of treatment, no difference was seen between the group receiving latrepirdine, 20 mg 3 times daily, and placebo. On the ADAS-cog, treated patients achieved a nonsignificant 0.1-point difference from those taking placebo (P = .86), and neither group was significantly changed from baseline.
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: The article above uses a research design to study HIV prevention with two different groups. Based on data collected in Africa and Thailand, there is a correlation between HIV viral load and HIV 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. The article suggests that ART may make HIV-infected people less contagious. 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 above is a between-subjects design with three groups concerning cognitive style, personality and vulnerability to postnatal depression. The researchers compared personality and cognitive style in women with recurring major depressive disorder who experienced one or more postnatal episodes. One group was a group of women with postnatal depression. A second group was healthy females with no preexisting disorders. The third group was women with recurrent major depressive disorder who experienced no perinatal episodes.
Random sampling
Definition: A sampling method in which individuals are selected so that each member of the population has an equal chance of being selected for the sample, in the selection of one member it is independent of another member of the population.
Example: http://www.weeklycalistogan.com/articles/2010/03/04/business/local/doc-4b8f0145460e1345680188.txt
Application: Random sampling was used in the above wine-grading arcticle, wherein ten wines were examined from three locations in one afternoon in Napa Valley, California. This was for the Premiere Napa Valley 2010 event.
Random Assignment
Definition: A method of assigning subjects to treatment groups so that any individual selected for the experiment has an equal probability of assignment to any of the groups in the assignment of one subject to a group that is not affect the assignment of any other individual to that same group.
Example: http://content.nejm.org/cgi/content/full/NEJMe1002322
Application: The global epidemic of type 2 diabetes has prompted a large number of clinical trials aimed at reducing its incidence. The Diabetes Prevention Program and its long-term outcome study, which are the only studies that can address comparative effectiveness since they included random assignment to lifestyle modification, a medication, and placebo, showed that lifestyle intervention had a substantially more powerful effect than did metformin when each was compared with placebo (a reduction in incident diabetes with lifestyle intervention of 58% at 3 years and 34% after 10 years vs. a reduction with metformin of 31% at 3 years and 18% after 10 years).
Independent Variable
Definition: A variable manipulated in an experiment to determine it's effect on the dependent variable.
Application: The cruise industry represents a small segment of the vacation industry which itself is a very small part of the leisure industry. The cruise market is characterized by exceptional value proposition, wide appeal, positive guest demographics, high guest satisfaction rate and favorable supply vs. demand balance. In their research, by combining SPSS Inc.'s data integration and analysis capabilities with relevant findings, they have predicted the future growth of the industry. They employed various significant variables that have an impact on this industry and created regression models with SPSS Base to determine the future direction of the industry. Before deploying the regression model, the relationship between several independent and the dependent variable was analyzed using standard SPSS output, including charts, tables and tests.
Levels of the Independent Variable
Definition: One value of the independent variable. To be a variable, an independent variable must take on at least two different levels.
Application: As noted for the dependent variable the above-mentioned cruise industry, while researching findings, they predicted future growth of the industry. Before deploying the regression model, the relationship between several independent and the dependent variable was analyzed using standard SPSS output, including charts, tables and tests.
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.
Application: In the above article, they examine that early marijuana use increases psychosis risk in young adults. The study looks at cannabis-psychosis association in sibling pairs to minimize confounding variables
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.
Example: http://psychservices.psychiatryonline.org/cgi/content/abstract/61/3/317
Application: The study noted above tested the effectiveness of a schizophrenia care management program for family caregivers of Chinese patients with schizophrenia in Hong Kong. A multisite controlled trial was conducted with 92 patient-caregiver dyads. They were randomly assigned to either the schizophrenia care management program or to usual care. The patients' symptoms, functioning, and length of rehospitalization and their families' perceived social support, expressed emotion, and functioning were measured at recruitment and at one month and 15 months after the intervention. The findings provide evidence that the multidisciplinary schizophrenia care program can improve the psychosocial functioning of patients and their families and social support of caregivers.
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 independent variable. In a within-subject designs, each subject receives each treatment condition. Also known as a repeated measures design or a treatment-by-subjects design.
Application: The research above notes that new autism prevention research reported from Hamamatsu University shows that statistical parametric mapping was used for between-subject analysis and within-subject correlation analysis with respect to clinical variables.
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 independent variable. In a within-subject designs, each subject receives each treatment condition. Also known as a repeated measures design or a treatment-by-subjects design.
Application: As noted in the aforementioned article, this article also noted the within-subjects design with three or more groups in connection to new autism prevention research reported from Hamamatsu University.
Main effect
Definition: The mean of all subjects given one level of independent variable ignoring the classification by other independent variable in a factorial design.
Example: http://www.informaworld.com/smpp/content~content=a785042995&db=all
Application: The article above looks at the problems in testing main effects when there is interaction are discussed. A method by which main effects can be tested independently of the interaction is developed and compared with the hierarchical method. The hierarchical method is shown to be inadequate, as it does not provide sufficient control of the type I error rate. The alternative method provides control of the type I error rate, but is quite conservative.
Interaction
Definition: A situation in a factorial design in which the effect of one independent variable depends on the level of the other independent variable with which it is combined.
Example: http://www.ncbi.nlm.nih.gov/pubmed/349428
Application: The article above looks at the observer interaction variable in evaluation of socializing properties of pimozide. Eighteen chronic, institutionalised patients were randomly assigned to two groups for the purpose of a double blind trial of pimozide. The results of the study indicated an increase in socialization, as measured by the Venables scale, for both groups, and no significant difference in this variable between placebo and active preparation groups.
Strength of Effect (Eta squared)
Definition: Eta-squared (η2) is a measure of effect size for use in ANOVA.
Example: http://www.helsinki.fi/~komulain/Tilastokirjat/Pierce_Block_Aguinis_Eff_Size.pdf
Application: In the article above, the authors provide a cautionary note on reporting accurate eta-squared values from multifactor analysis of variance (ANOVA) designs. They reinforce the distinction between classical and partial eta-squared as measures of strength of association. They provide examples from articles published in premier psychology journals in which the authors erroneously reported partial eta-squared values as representing classical eta squared values. Finally, they discuss broader impacts of inaccurately reported eta squared values for theory development, meta-analytic reviews, and intervention programs.
Scatterplot
Definition: A scatterplot is a useful summary of a set of bivariate data (two variables), usually drawn before working out a linear correlation coefficient or fitting a regression line. It gives a good visual picture of the relationship between the two variables, and aids the interpretation of the correlation coefficient or regression model.
Example: http://www.bucem.com/2010/2/24/1310538/how-will-freeman-fare-in-the
Application: In the article above, the to give the reader an idea in visual form, the researchers utilize a scatterplot that will help demonstrate exactly where their findings fell.
Positive relationship
Definition: A relationship between two variables in which, as the value of one variable increases, the value of the other variable tends to decrease also.
Example: http://www.renalandurologynews.com/glycemic-control-in-diabetic-esrd-patients/article/165496/
Application: The goals of diabetes care for patients with CKD/end-stage renal disease would seem to be similar to the goals of care for diabetic patients in general: control of hyperglycemia and its symptoms, prevention of microvascular and macrovascular complications, maintenance of overall health status and quality of life, and avoidance of hypoglycemia. In their research, doctors noted that a strong positive relationship exists between HbA1c and mean plasma glucose levels in the general population, with each one percentage point rise in HbA1c reflecting a change of about 35 mg/dL in mean plasma glucose.
Negative relationship
Definition: A relationship between two variables in which, as the value of one variable increases, the value of the other value tends to decrease.
Example: http://www.egovmonitor.com/node/34009
Application: In the article above, the author discussed the current macroeconomic framework. He focuses on the institutional aspects that have proved successful, in particular, from the European perspective. These are central bank independence, the centrality of price stability for monetary policy and the need to adopt a medium-term, rules-based perspective in the conduct of monetary and fiscal policies. The financial crisis has not contested or discredited these three principles. Empirical evidence confirms this negative relationship, with a 100 basis point permanent increase in inflation being associated with a 10-30 basis point decrease in trend output growth. Hence, if this is applied to the euro area, a 4% inflation target would shave no less than half a percentage point per year off trend growth!
No relationship
Definition: A relationship between two variables in which there is no relationship between them.
Example: http://www.miller-mccune.com/science-environment/storks-vaccines-and-causation-10195/
Application: The article above notes that a major study in 2002 of almost half a million Danish children found that no difference in immunization records between those children with or without autism. Currently, there are no scientific findings that a causal connection between immunization vaccines and autism exists. Further, due to Denmark we have the research on this spurious relationship between autism and the MMR vaccine.
Linear relationship
Definition: A relationship between two variables that can be described by a straight line.
Application: The research above notes that as the brain volume decreases by nearly 2 percent a decade as people age, a US study has found a significant negative linear relationship between alcohol consumption and the volume of the brain and the space it takes up.
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: As noted in the article above, it is a widely-accepted belief that can be found in some form or other in most Western cultures. In England it as ‘Beer before wine is fine, wine before beer—oh dear!’ Anywhere groups of people gather together to partake in that age-old pastime of drinking too much this little ditty is often passed around as solid advice. One study that took place back in the golden age 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 of R(squared) indicating the common variants of variables X and Y.
Example: http://www.hotelnewsnow.com/articles.aspx?ArticleId=2792&PageType=News&ArticleType=35
Application: The article above states that the STAR report provides the most meaningful benchmarking data in the [body building] industry, but in order to protect data confidentiality, reports must include at least four competitors, some of which may be less comparable and/or competitive than others in the set. Once included, all properties in the competitive set are treated as equal; each property is considered 100 percent competitive against one another. However, a new tool allows you to see your competitive strength in a way never seen before. 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 explained by the variations in your market.
Correlation does not equal causation
Definition: "Correlation does not equal causation" is a phrase used in science and statistics to emphasize that correlation between two variables does not automatically imply that one causes the other (though it does not remove the fact that correlation can still be a hint, whether powerful or otherwise).
Example: http://www.americanbanker.com/usb_issues/120_3/cold-turkey-on-hot-money-1014706-1.html
Application: The article above states that the observation that correlation does not equal causation has been put in the service of some sketchy claims in the past. It was a longtime favorite of the tobacco industry, which argued for decades that lots of smokers dying of lung cancer did not prove smoking causes cancer.
Extra-Credit (3 points each)
Normal Distribution
Definition: The normal distribution is a continuous probability distribution that often gives a good description of data that cluster around the mean.
Example: http://www.theepochtimes.com/n2/content/view/31233/
Application: In the article above, research is done concerning whether or not the L.A. School District is subject to Civil Rights Review for English Learner Students. In this study, a high rate, the study concludes, cannot plausibly be due to the lack of cognitive skills and ability among these students, stating, “some may assert that cognitive skills or ability are affecting learning outcomes. However, this is not plausible; a rate of 29 percent defies the normal distribution of cognitive skills that education researchers assume in any given population, and research suggests that ELs need five to seven years to learn English with native fluency
Symmetrical
Definition: A distribution in which observations equidistant from the central maximum have the same frequency.
Example: http://bjp.rcpsych.org/cgi/content/abstract/196/3/173
Application: In the above study, the researcher notes that it is not clear whether the effects of cognitive–behavioural therapy and other psychotherapies have been overestimated because of publication bias. The researcher's aim is to examine indicators of publication bias in randomised controlled trials of psychotherapy for adult depression. And the method used was to examine 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.
Asymptotic
Definition: Is a precise and well-defined concept of balance or "patterned self-similarity" that can be demonstrated or proved according to the rules of a formal system.
Example: http://www.usatoday.com/sports/football/nfl/2009-12-02-2054713109_x.htm
Application: The only article that I could find concerning asymptotic balance was in the above article, wherein the National Football League adopted a new policy states, which in part states that: "Once removed for the duration of a practice or game, the player should not be considered for return-to-football activities until he is fully asymptotic, both at rest and after exertion, has a normal neurological examination, normal neuropsychological testing, and has been cleared to return by both his team physician(s) and the independent neurological consultant." Though not statistically speaking, the term is used with the overarching definition above.
Continuous
Definition: It means numerical data which can hold any value in a study.
Example: http://www.grandforksherald.com/event/article/id/154289/
Application: In the article above, researchers installed two different types of implants in bears. The one type, provides three years of continuous data on heart rates. The other offers more detailed information on the heart’s electrical signals, but only during the short window when the bear is roused from hibernation and sedated.
Sampling Error
Definition: Sampling Error is the error caused by observing a sample instead of the whole population. The sampling error can be found by subtracting the value of a parameter from the value of a statistic.
Example: http://www.gallup.com/poll/126338/Obama-Retains-Trust-Congress-Healthcare.aspx
Application: In a study (noted above) to gauge the the trust that the country still retains for President Obama, a study was conducted and the 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 null hypothesis is a hypothesis (within the frequentist context of statistical hypothesis testing) that might be falsified using a test of observed data.
Example: http://www.medscape.com/viewarticle/718270
Application: In a study, found in the article above, researchers attempt to find how effective antidepressants are. In critiquing the study, critics argue that some of the authors purposely excluded studies that involved an initial, single-blind, lead-in phase, attempting to remove early placebo-responders. However, in doing so they further reduced the potential for identifying drug-placebo differences and increased the possibility of favoring the null hypothesis (ie, no difference between drug and placebo).
Alternative Hypothesis
Definition: The alternative hypothesis and the null hypothesis are the two rival hypotheses which are compared by a statistical hypothesis test.
Example: http://dailycaller.com/2010/03/10/would-you-let-the-n-y-times-teach-your-kids-about-global-warming/
Application: The article above criticizes and argues that American students lag behind many of their peers in other countries in various subjects, given perhaps to the fact that too many teachers get lesson plans from the New York Times. The author argues that instead of adding to this sense of fear [in this instance, to the subject of global warming], the New York Times might have encouraged students to consider the role that skepticism is supposed to play in the scientific process, and the importance of scientists disclosing their data so that others can assess their logic and consider alternative hypothesis.
Significance level
Definition: In statistics, a result is called statistically significant if it is unlikely to have occurred by chance.
Example: http://content.nejm.org/cgi/content/full/NEJMoa1001286
Application: As noted before, the ACCORD Study Group investigated whether therapy targeting normal systolic pressure reduces major cardiovascular events in participants with type 2 diabetes at high risk for cardiovascular events. One of the findings that the ACCORD Study Group found was a significance level of less than 0.05, intensive blood-pressure management did reduce the rate of two closely correlated secondary outcomes — total stroke and nonfatal stroke. Assuming that this finding was real, the number needed to undergo intensive blood-pressure management to prevent one stroke over the course of 5 years was 89.
Two-tailed test
Definition: The two-tailed test is a statistical test used in inference, in which a given statistical hypothesis, H0 (null hypothesis) will be rejected when the value of the statistic is either sufficiently small or sufficiently large.
Example: http://www.orthosupersite.com/view.aspx?rid=61001
Application: The article above discusses that previous studies have reported that advancing age does not significantly affect acute inpatient stay in femoral neck fractures. The primary goal of their study was to compare inpatient stay in acute orthopedic wards and time delay to surgery with increasing age in patients with femoral neck fractures. In their method of research, their P values were estimated using the likelihood ratio test statistic. An arbitrary level of 5% statistical significance (two-tailed) was assumed.
One-tailed test
Definition: A one-tailed test finds if the null hypothesis is rejected only for values of the test statistic falling into one specified tail of its sampling distribution.
Example: http://www.cbsnews.com/stories/2008/10/11/politics/uwire/main4514928.shtml
Application: The article above discusses a study made during President Obama's presidential race, wherein opponents to Obama mercilessly attacked him for not having enough experience. Detractors claim that McCain's military service and 21 years as a senator make him more likely to be a good executive team [along with Palin]. The test was one-tailed for greater sensitivity because the prediction is not just that experience matters, but that it makes a president better.
Degrees of Freedom
Definition: Is the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.
Application: In discussing Microsoft's new Natal Software for their XBOX 360, the author notes that the new gaming console's software is capable of almost instantly inferring a subject's motion, which is reflected by an onscreen avatar in a game. That's a lot of fast number-crunching: Microsoft figures there are something like 10 to the 23rd power "degrees of freedom," or possible positions, for a human body.
Type I Error
Definition: Type I error, also known as an "error of the first kind", an α error, or a "false positive"; the error of rejecting a null hypothesis when it is actually true.
Example: http://www.medscape.com/viewarticle/717505
Application: The article above discusses all management strategies for urinary tract infections (UTIs), and how they achieve similar symptom control, according to the results of a randomized controlled trial reported in the February 5 issue of the BMJ. Limitations of this study include possible type I error for the subgroup analyses; slight but not significant difference among groups in frequency symptoms at baseline; and some group differentiation in dipstick use, midstream urinalysis, and the willingness of women to delay the use of antibiotics.
Type II Error
Definition: Type II error, also known as an "error of the second kind", a β error, or a "false negative"; the error of failing to reject a null hypothesis when it is in fact not true.
Example: http://goliath.ecnext.com/coms2/gi_0199-4717191/Multicollinearity-and-measurement-error-in.html
Application: The article above discusses that literature on structural equation models is unclear on whether and when multi-collinearity may pose problems in theory testing (Type II errors). Two Monte Carlo simulation experiments show that multi-collinearity can cause problems under certain conditions.
Power
Definition: Number or percentage that indicates the probability a study will obtain a statistically significant effect.
Example: http://sports.insidepulse.com/2010/02/25/inside-pulse-sports-hall-of-fame-5-mark-mcgwire/
Application: The article above discusses the career of baseball player Mark McGwire. Aside from being a somewhat biography of his career, it does note that the “Big Mac” was the standard for home runs and nearly every power statistic for most of his 16 year career. Baseballs uses the principal of power statistics when measuring a player's accuracy at-bat.
Pairwise comparisons
Definition: Pairwise comparison generally refers to any process of comparing entities in pairs to judge which of each pair is preferred, or has a greater amount of some quantitative property.
Example: http://www.nashuatelegraph.com/news/654955-196/rule-in-most-elections-is-1-man.html
Application: The article above mentions pairwise comparison when discussing voting methods. The author states that people around the state will cast ballots to elect officials during voting season, and that they include “Borda counts,” in which voters give various points to every candidate and the candidate with the highest point total wins; “pairwise comparison,” a labor-intensive method in which voters compare every candidate to every other candidate.
Post-hoc comparisons
Definition: The logical fallacy of believing that temporal succession implies a causal relation.
Example: http://www.theheart.org/article/1056401.do
Application: The article above tells how patients on amiodarone for maintenance of sinus rhythm after cardioversion of atrial fibrillation (AF) who are looking to switch to dronedarone in most cases can safely begin taking the newer antiarrhythmic agent within two days of stopping the older one, according to a post hoc analysis of two randomized trials. Further, Kowey, who cautioned that the post hoc analysis is based on a fairly small population and can be only hypothesis-generating, was to present it here today at the American College of Cardiology 2010 Scientific Sessions/i2 Summit.
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