PSY302-300603204
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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: In patients with type 2 diabetes at high risk for cardiovascular events, targeting a systolic blood pressure of less than 120 mm Hg, as compared with less than 140 mm Hg, did not reduce the rate of a composite outcome of fatal and nonfatal major cardiovascular events. Baseline characteristics were compared between study groups with the use of the chi-square test, Fisher's exact test, Wilcoxon rank-sum test, and two-sample t-tests
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.sciencedaily.com/releases/2007/07/070701094054.htm
Application: suicide attempts declined during the first month of treatment--whether that treatment consisted of medication, psychotherapy, or both.
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: 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. Diet with acids and tannin did not improve the growth performance of grower pigs but had no deleterious effects on selected blood parameters. The possibility of beneficial effects of adding acids and tannin in diets on growth performance over a longer period, however, could not be excluded.
Two-Way ANOVA test
Definition: Testing the relationship between two categorical independent variable and a continuous independent variable.
Application: The reliability of the measurements was analyzed using 2-way ANOVA intraclass correlation coefficients (ICC), 95% confidence intervals (CI) and standard error of measurement (SEM) for precision, for a single measurement [ICC(single)] and the average of 3 measures [ICC(average)].
Correlation test
Definition: Testing the relationship between two continuous variables, either of which can be considered the independent or dependent variable.
Example: http://www.docguide.com/news/content.nsf/news/852576140048867C852576E5007905C9
Application: The data indicated a statistically significant correlation (P = .013) between folate deficiency and Diagnostic and Statistical Manual of Mental Disorders (Fourth Edition) dementia criteria.
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/NEJMoa1001282
Application: Baseline characteristics were compared between study groups with the use of the chi-square test, Fisher's exact test, Wilcoxon rank-sum test, and two-sample t-tests
Concepts
Standard Score
Definition: A score obtained by using the transformation z = (X-X)/s
Application:
The current weightings—assigned by indicator—can be found here. A more complicated but widely used standardization or normalization method has been adopted involving z-scores.
Confidence Interval
Definition: A range of score values expected to contain the value of mu with a certain level of confidence.
Example: http://www.gallup.com/poll/126602/Taliban-Increasingly-Unpopular-Pakistan.aspx
Application: For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±3.7 percentage points.
Parametric Test
Definition: A statistical test involving hypotheses that state a relationship about a population parameter.
Example: http://www.emaxhealth.com/1506/100/35994/red-meat-obesity-raise-risk-colon-cancer.html
Application: A team from the Division of Cancer Epidemiology and Genetics at the US National Cancer Institute (NCI) in Rockville MD reviewed data from a cohort of over 300,000 men and women and reviewed the detailed questionnaires by the participants about the types of meat that they consumed and how it was cooked. After seven years of follow-up, there were 2,710 cases of colon cancer in the group. This is a parametric test since it involves a pop parameter.
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.
Example: http://content.nejm.org/cgi/content/full/NEJMoa1001282
Application: 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.
Statistically significant difference
Definition: The observed value of the test statistic falls into a rejection region and the Null Hypothesis is rejected.
Example: http://www.reuters.com/article/idUSN1417954520100314?type=marketsNews
Application: Among patients who received the MitraClip, 9.6 percent suffered major adverse events compared with 57 percent in the surgery group, a difference considered to be highly statistically significant.
Nonsignificant difference
Definition: the observed value of the test statistic does not fall into a rejection region and the null hypothesis is not rejected.
Example: http://www.businessweek.com/lifestyle/content/healthday/636909.html
Application: A first comparison found that the control group had a 20 percent higher need to repeat the operation because of mechanical failure of the knee (from wear, fracture or loosening) compared to the sport group. But when they took into account other health problems such as obesity or diabetes, the sport group had a 10 percent higher risk of mechanical failure compared to the control group, but the difference wasn't statistically significant
Between-subjects Design, with two groups
Definition: An experiment in which two or more groups are created.
Example: http://www.businessweek.com/lifestyle/content/healthday/636909.html
Application: In fact, the sport group had slightly higher knee function scores than the control group
Between-subjects Design, with three or more groups
Definition: An expirement in which tow or more groups are created.
Example: http://www.medscape.com/viewarticle/717505
Application: Women who immediately took antibiotics had 3.5 days of moderately severe symptoms. The 5 groups did not differ significantly in duration or severity of symptoms. Mean frequency of symptoms on a scale of 0 to 6 was 2.15 for immediate antibiotics, 2.08 for midstream urinalysis, 1.74 for dipstick, 1.77 for symptom score, and 2.11 for delayed antibiotics (likelihood ratio test for the 5 groups: P = .177).
Random sampling
Definition: A sample in which individuals are selected so that each member of the population has an equal chance of being selected for the samlple, and the selction of one member is independednt of the selecting of any other member of the population.
Example: http://www.123jump.com/economy-story/February-Retail-Sales-Rise-0.3/37092/
Application: A stratified random sampling method is used to select approximately 5,000 retail and food services firms whose sales are then weighted and benchmarked to represent the complete universe of over three million retail and food services firms
Random Assignment
Definition: A method of assigning subjects to treatment groups so that any individual selected for the expirement 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 individual to that same group.
Example: http://content.nejm.org/cgi/content/full/NEJMoa1001286
Application: The ACCORD BP trial was a nonblinded trial in which participants were randomly assigned to intensive therapy that targeted systolic blood pressures of less than 120 mm Hg or standard therapy that targeted systolic blood pressures of less than 140 mm Hg.
Independent Variable
Definition: A variable manipulated in an experiment to determine its effect on the dependent variable.
Example: http://www.orthosupersite.com/view.aspx?rid=61001
Application: The independent variable in this study is age.
Levels of the Independent Variable
Definition: A variable manipulated in an experiment to determine its effect on the dependent variable.
Application: The placebo would be a level of an 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.docuticker.com/?p=32669
Application: In two large surveys of diverse populations, we found that people are more likely to form close platonic and romantic relationships with other people of the same birth order. This effect cannot be explained by confounds of family size.
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://www.orthosupersite.com/view.aspx?rid=61001
Application: The Dependent varible was hospital stay, Delay to surgery and acute care costs.
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 within subject design, each subject receives each treatment condition also known as a repeated measures design or a treatment by subjects design.
Example: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1279893/
Application: We investigated the effects of two teaching variables on students' Spanish vocabulary quiz performance: (a) group study and (b) individual versus group contingencies.
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 within-subjects design, each subject receives each treatment condition. Also known as a reapeated measures design or a treatment by subjects design.
Example:
Application:
Main effect
Definition: the mean of all subjects given one level of the indepent variable ignoring the classification by the other independent variable in a factorial design.
Example: http://www.docguide.com/news/content.nsf/news/852576140048867C852576D90068628F
Application: 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 the effect of one independent varible depends on the level of the other independent variable with which it is combined.
Example: http://www.cardiosource.com/cjrpicks/CJRPick.asp?cjrID=5735
Application: In addition,the investigators observed a possible interaction according to the lipid subgroup, with a potential benefit for patients with both high triglycerides and low HDL-C levels at baseline (p = 0.057 for interaction).
Strength of Effect (Eta squared)
Definition: The size of the effect on the independent variable.
Example: http://allnurses.com/nursing-articles/t-tests-one-378029.html
Application: The magnitude of the differences in the means (mean difference = 3.49, 95% CI: -1.80 to 1.87) was very small (eta squared = .008).
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 verticle axis.
Example: http://www.heraldsun.com.au/news/learn/steady-approach/story-e6frf7nf-1225838982226
Application: You may have studied that the process of fitting a line of best fit, linear regression, is only appropriate if the data produces a linear (straight) scatterplot. The data points for larger values of the dependent variable, however, can be 'dragged' lower, and closer to a straight line if the vertical axis uses a logarithmic scale. This can be achieved by performing a log transformation on the y value.
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 increase also.
Example: http://www.eurekalert.org/pub_releases/2010-03/wfub-vdl031110.php
Application: The study is the first to show a positive relationship between calcified plaque in large arteries, a measure of atherosclerosis or "hardening of the arteries," and circulating vitamin D levels in black patients.
Negative 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.
Example: http://www.docuticker.com/?p=32536
Application: Previous literature has found a negative relationship, studying as channels of transmission the role of exports, substitution of factors of production, terms of trade, openness, and productivity.
No relationship
Definition:Variables that do not increase or decrease in relation to another.
Application: Analysis of the most comprehensive list of stimulus spending to date found no relationship between where the money is going and unemployment and poverty.
Linear relationship
Definition: A relationship between two variables that can b e described by a straight line.
Example: http://www.hotelnewsnow.com/articles.aspx?ArticleId=2792&PageType=News&ArticleType=35
Application: The multiple regression analysis output comes in the form of a linear equation, which is analogous to an improved competitive set performance metric.
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: 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 r2 indicating the common variance of variables X and Y.
Example: http://www.hotelnewsnow.com/articles.aspx?ArticleId=2792&PageType=News&ArticleType=35
Application: 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.
Correlation does not equal causation
Definition: 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://blogs.discovermagazine.com/intersection/2010/02/27/politics-religion-sex-and-intelligence/
Application: Of course many of the factors considered will show interesting correlations in a sample, but correlation does not equal causation. Each is extremely dependent on social mores, cultural norms, hormones, relationships, socieoeconomic status, and much, much, more.
Extra-Credit (3 points each)
Normal Distribution
A theoretical mathematical distribution that specifies the relative frequency of a set of scores in a population.
http://www.theepochtimes.com/n2/content/view/31233/
Application: This 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
A frequency distribution that when folded at a midpoint produces two halves identical in shape.
Asymptotic
Definition:approaching a given value as an expression containing a variable tends to infinity
Example: http://www.psychwiki.com/index.php?title=PSY302-300603204&action=edit§ion=39
Application: This stereotype, however, is inherently asymptotic: no matter how earnestly one tries, its realization perpetually eludes, then leaves one feeling inadequate for failing to make the grade.
Continuous
Definition: A variable that can take on an indfinite set of values between the limits of the variable.
Sampling Error
Definition: The amount by which a sample mean differs from the population mean
Example: http://www.gallup.com/poll/126602/Taliban-Increasingly-Unpopular-Pakistan.aspx
Aplication: Results are based on face-to-face interviews with 1,000 adults, aged 15 and older, conducted Sept. 20 to Oct. 12, 2009, and 1,000 adults in June 4-16, 2009, in Afghanistan. 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 a 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://www.medscape.com/viewarticle/718270
Application: identifying drug-placebo differences and increased the possibility of favoring the null hypothesis (ie, no difference between drug and placebo).
Alternative Hypothesis
Definition:A statement of what must be true if the null hypothesis for a statistical test is false.
Example:http://dissidentvoice.org/2010/03/the-washington-post-on-lunatic-911-conspiracy-theorists/
Application: NIST also completely ignored the actual leading alternative hypothesis, which was that a substance called thermite (or its U.S. Department of Defense-patented variation, thermate) may have been used to cut the building’s columns, rather than, or in conjunction with, traditional explosive demolitions.
Significance level
Definition: A probability value that provides the criterion for rejecting a null hypothesis in a statistical test. Example: http://news.google.com/news/search?aq=f&pz=1&cf=all&ned=us&hl=en&q=Significance+level Application: At a significance level of less than 0.05, intensive blood-pressure management did reduce the rate of two closely correlated secondary outcomes
Two-tailed test
Definition:A statistical test using rejection regions in both tails of the sampling distribution of the stes statistic. Also called a nondirectional test.
Example:http://www.orthosupersite.com/view.aspx?rid=61001
Application: P values were estimated using the likelihood ratio test statistic. An arbitrary level of 5% statistical significance (two-tailed) was assumed. We did not adjust P values for multiple comparisons.
One-tailed test
Definition: A statistical test employing a rejection region in only one tail fo the sampling distribution of the test statistic. Also called directional test.
Degrees of Freedom
Definition: The number of scores free to vary when calculating a statistic.
Example: http://www.gizmag.com/twendy-one-robot-elderly/14496/
Application: To maximize dexterity Twendy-One’s four-finger-hand has 13 degrees of freedom.
Type I Error
Definition: The error in statistical decision making that occurs if the null hypothesis is rejected when actually it is true of the population.
Example: http://www.medscape.com/viewarticle/717505
Application: 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: The error in statistical decision making that occurs if the null hypothesis is not rejected when it is false and the alternative hypothesis is true.
Application: 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. the null was not rejected when it was false.
Power
Definition: The probability of rejecting the null hypothesis when the null hypothesis is false and the alternative hypothesis is true. The power of a statistical test is given by 1-B.
Pairwise comparisons
Definition: Statistical comparisons involving two means
Application: Through the progressive integration of many pairwise comparisons, this approach generates a single consensus spectrum as an output that is then used to adjust the chemical shift positions of the peaks from the original input spectra to their final aligned positions.
Post-hoc comparisons
Statistical tests that make all possible pairwise comparisons after a statistically significant Fobs has occured for the overall analysis of variance.
http://content.nejm.org/cgi/content/full/NEJMoa1001286
The United Kingdom Prospective Diabetes Study13,14 and a post hoc subgroup analysis of the Hypertension Optimal Treatment (HOT) trial15,16 showed reductions in cardiovascular events with antihypertensive therapy among patients with type 2 diabetes mellitus, but the participants in their intensively treated groups had much higher mean systolic blood-pressure levels (144 mm Hg in both cases) than did the participants in either group of our trial.
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