PSY302-300624706
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://www.biomedcentral.com/1471-2105/8/211
Application: In this article, wanted to characterize a group of related non-homologous proteins by statistically identifying significant patterns of amino acid enrichment or depletion. Composition Profiler will test all groupings of amino acids according to the listed properties for statistically significant differences between the two samples, when run in discovery mode. The discovery mode uses a two-sample t-test between two sequences of binary indicator variables.
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: According to a two-sample t-test, studying the effect of commercial viewing on attitudes toward an oil company, the null hypothesis was rejected, finding that there was no significance 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.
Example: http://www.chiroaccess.com/Articles/Children-Backpacks-and-Back-Pain.aspx?0000125
Application: In the article, the study was conducted to measure increase backpack loads for kids and the effect it has on the childrens' lumbar spine. A one-way ANOVA test was used to show that backpack loads significantly increased lumbar asymmetry (P < 0.03).
Two-Way ANOVA test
Definition: Testing the relationship between two categorical independent variable and a continuous independent variable.
Application: The study in this article argues that "highly effective leaders are distinguished by the ability to select and apply one of four leadership styles most fit to influence a follower's readiness level. Inherent in each leadership style is a mix of decision methods and communication techniques to influence a follower to perform a task or achieve a goal. SLT predicts that a match of style and readiness contributes to higher measures of follower satisfaction and leader effectiveness than a mismatch of style and readiness contributes." "Two-way ANOVA tests for the main and interactive effects of leadership styles and leader adaptability on meeting management effectiveness provided support for the main effects only."
Correlation test
Definition: Testing the relationship between two continuous variables, either of which can be considered the independent or dependent variable.
Application: In this article about "internalized homophobia," the researchers found a very small relationship between internalized homophobia and sexual risk taking. A correlation of .10, a percentage of 5.3 percent. They also found that the correlation got smaller over time. The correlation dropped .02 for every year since 1988.
Chi-square test
Definition: Testing the relationship between two categorical variables, either of which can be considered the independent or dependent variable.
Application: The purpose of this study was 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. The researchers compared clinical and sociodemographic variables by statin and NSAID use, using chi-square tests and multinomial logistic regression. They examined associations between medications and comorbid illness with mortality using unadjusted and adjusted Cox proportional hazard models.
Concepts
Standard Score
Definition: A score obtained by using the transformation z=(X-Xbar)/S.
Example: http://www.businessweek.com/lifestyle/content/healthday/634967.html
Application: Researchers followed 767 people out of a large study who were caring for a spouse with any disabling condition. "The spouses who had the highest scores for strain had the highest risk scores for stroke," said William E. Haley. Strain was measured on a standard score by asking the participants how many days during the past week they had felt depressed, lonely, sad or had crying spells. A high score on the measure of strain was associated with a 23 percent higher risk of stroke. The association was stronger in husbands than in wives.
Confidence Interval
Definition: A range of score values expected to contain the value of mu with a certain level of confidence.
Application: Based on the data provided in this article about the average price per barrel, the range of the 95-percent confidence interval for the March 2010 futures price were $66 per barrel and $102 per barrel. Also, last year, the market participants thought that March-delivered WTI into Cushing, Oklahoma, would be priced at $50 per barrel. However, the implied instability of 87 percent was more than twice the current level, resulting in a range of $29 and $87 per barrel, for the 95-percent confidence interval.
Parametric Test
Definition: A statistical test involving hypotheses that state a relationship about a population parameter.
Application: "This study investigated the relationship between Big Five Personality traits, gender, and infidelity in dating relationships. Big Five Personality traits were determined by the Big Five Mini-Modular Markers (3M40) and participants were characterized by scoring either high or low on the five bipolar subscales: Extraversion, Agreeableness, Conscientiousness, Neuroticism, and Openness to Experience. Infidelity, which was measured by dimensions of both emotional and physical infidelity exclusively and combined, was measured using the Infidelity Scale. Relationship satisfaction was also measured, using the Relationship Assessment Scale (RAS) to better understand the motivations behind infidelity. The sample consisted of 160 adults (Men = 53, Women = 107) adults who lived in the United States for a minimum of five years, between the ages of 18 to 30 years old, who were in a dating relationship which his/her partner perceived as exclusive for at least 3 months. Participants were recruited and measures were administered via the Internet. The relationship between gender and infidelity was analyzed using a series of Kruskal Wallace Tests. The relationship between gender and infidelity was analyzed using a Spearman's Rho Correlations. The relationship between Big Five Personality Traits and Infidelity was also analyzed using a Spearman's Rho Correlations. To understand the best predictor of infidelity in this sample a series of Multiple Regressions were conducted inputting demographic variables, Big Five personality traits, and relationship satisfaction. In addition, comparisons between men and women on demographic variables were analyzed using a series of both parametric and non-parametric tests. As predicted, this study found a significant negative correlation between relationship satisfaction and emotional and physical infidelity. Contrary to the hypotheses of this study, there were no significant gender differences found for emotional and physical infidelity. Contrary to hypotheses, for females, there was no significant association between Neuroticism and infidelity. Only part of the personality and gender hypotheses was supported for males; Extraversion was positively associated to infidelity, while Conscientiousness was negatively associated to infidelity. Low relationship satisfaction was the best predictor for infidelity in this sample. (PsycINFO Database Record (c) 2010 APA, all rights reserved)"
Nonparametric Test
Definition: A statistical test involving hypotheses that do not state a relationship about a population parameter. AKA distribution-free test.
Application: This study was "to examine the feasibility and level of acceptability of a mindful yoga intervention provided during pregnancy and to gather preliminary data on the efficacy of the intervention in reducing distress." "Outcomes were evaluated from pre- to postintervention and between second and third trimesters with repeated measures analysis of variance and post hoc nonparametric tests." "Women practicing mindful yoga in their second trimester reported significant reductions in physical pain from baseline to postintervention compared with women in the third trimester whose pain increased. Women in their third trimester showed greater reductions in perceived stress and trait anxiety. Preliminary evidence supports yoga’s potential efficacy in these areas, particularly if started early in the pregnancy."
Statistically significant difference
Definition: The observed value of the test statistic falls into a rejection regionand Ho is rejected.
Example: http://latimesblogs.latimes.com/booster_shots/2010/01/soda-tax-new-york-california.html
Application: A Boston study of 103 high schoolers found that those who consumed diet sodas for 25 weeks didn’t lose weight compared with kids who drank regular soda. However there was a statistically significant difference for the one-third of kids with the highest BMIs.
Nonsignificant difference
Definition: The observed value of the test statistic does not fall into a rejection region and null hypothesis is not rejected.
Example: http://www.medpagetoday.com/PrimaryCare/DietNutrition/18131
Application: A study showed that total cholesterol declined by an average of 8.9 mg/dL with the low-fat diet versus a decrease of 3.8 mg/dL in the low-carb group. A similar but also nonsignificant difference was seen in LDL cholesterol. Triglyceride levels actually declined more with the low-carb diet.
Between-subjects Design, with two groups
Definition: An experiment in which two groups are created.
Example: http://www.hptn.org/research_studies/hptn052.asp
Application: The study in this article is a between-subjects design about HIV prevention with two different groups to determine the effectiveness of two treatment strategies in preventing the sexual transmission of HIV in HIV-serodiscordant couples..
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: This study is a between-subjects design with three groups about cognitive style, personality and vulnerability to postnatal depression. The researchers compared personality and cognitive style in women with recurrent major depressive disorder who had experienced one or more postnatal episodes. One group was a group of women with postnatal depression. A second group was healthy female controls. The third group was parous 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, and the selection of one member is independent of any other member of the population.
Example: http://www.cbsnews.com/stories/2010/01/10/sunday/main6078219.shtml
Application: The poll in this article was conducted among a random sample of 1048 adults nationwide, interviewed by telephone December 17-22, 2009. Phone numbers were dialed from random digit dial samples of both standard land-line and cell phones.
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 and the assignment of one subject to a group does not affect the assignment of any other individual to that same group.
Example: http://www.medscape.com/viewarticle/716027
Application: In the study in this article, at 13 centers, 852 women with a history of spontaneous singleton preterm birth and a current singleton conception were randomly assigned to either a daily omega-3 supplement or matching placebo from 16 to 22 through 36 weeks of conception.
Independent Variable
Definition: A variable manipulated in an experiment to determine its effect on the dependent variable.
Example: http://abcnews.go.com/Technology/wireStory?id=9492635
Application: In this study, the independent variable is the parental education. Using data from birth records, the researchers found a strong relationship between parental education and high rates of autism.
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.
Example: http://www.gallup.com/poll/126065/Makes-700-Million-Adults-Migrate.aspx
Application: In this article, the researchers analyzed people's desires to migrate using several levels of the 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.
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: This article reports that the latest study evaluated the impact of abacavir therapy and the risk of hospitalization because of heart attacks among 2,930 HIV-positive patients in Denmark. The researchers didn’t only look for the occurrence of heart attacks among the volunteers, but they also looked for the same confounding variables—such as age, gender, elevated blood lipid levels, high blood pressure and the presence of other diseases known to be associated with CVD risk—that were included in more recent studies.
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://abcnews.go.com/Technology/wireStory?id=9492635
Application: In the research study, the researchers investigated the level of autism in California. The researchers identified those California babies that were diagnosed with autism disorder. In this study, autism was the dependent variable.
Within-subjects Design, with two groups
Definition: A research design in which two groups of subjects are exposed to and measured under each level of an independent variable. In within-subject design, each subject receives each treatment condition.
Example: http://www.prepme.com/about/scoreIncreaseReport
Application: Researchers “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 three or more groups of subjects are exposed to and measured under each level of an independent variable. In within-subject design, each subject receives each treatment condition.
Example: http://psychservices.psychiatryonline.org/cgi/content/full/53/2/210
Application: “The study compared clinicians' perceptions of three groups of veterans with posttraumatic stress disorder (PTSD): those seeking compensation for PTSD, those not seeking compensation, and those certified as permanently disabled and thus not needing to reapply for benefits. A within-subject design was used in this study. Participants responded to the same set of questions in reference to three groups of patients with PTSD who differed in their compensation-seeking status. These three groups were the non-compensation-seeking group, defined as veterans who were not seeking service-connection benefits for the first time or were not seeking an elevation of their service-connection status and were not rated as permanently disabled as a result of PTSD; the compensation-seeking group,defined as veterans who were seeking service-connection benefits for the first time, were applying for an elevation of their service-connection status, were appealing a rejected claim, or were applying for permanent status; and the permanent compensation group, defined as veterans who were certified as permanently disabled because of PTSD and thus were awarded compensation without being subject to reevaluation.”
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: According to a study presented here at the 2010 Society for Research on Nicotine and Tobacco Annual Meeting, Varenicline may acutely decrease smokers' enjoyment of smoking, but not smoking reinforcement. “Study measures including rating smoking behavior with a pocket topography device, which measures the number of puffs and total puff volume, and the smokers' subjective rating of their cigarettes, which included how much they liked the cigarette, how much nicotine the cigarette contained, and whether it was similar to their own brand. 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 behavior. For liking and number of puffs, the main effects were significant for quit interest and for sex. Liking and number of puffs were lower in those with high versus low interest in quitting, and in women versus men.”
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.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 person 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: A statistic that is a measure of the strength of effect.
Application: "The purpose of this study was to examine the impact of four incentive paths on third graders’ reading vocabulary and comprehension achievement and recreational and academic reading attitude. One hundred and twenty third-grade students were assigned to one of four incentive path treatment conditions. Data were analyzed using analysis of covariance (ANCOVA) with Fisher’s least significant difference (LSD) post hoc comparisons. An effect size of .09 was calculated using a partial η² (eta squared) statistic. Findings indicated that the four incentive path treatment conditions did not differentially impact student vocabulary, comprehension, and recreational reading. A significant difference for students’ academic reading attitudes was identified across the four incentive path treatment conditions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)"
Scatterplot
Definition: A plot of a bivariate distribution in which the x variableis plotted on the horizontal axis and the y variable is plotted on the vertical axis.
Example: http://economix.blogs.nytimes.com/2010/01/27/job-juggling-and-job-loss/
Application: This article includes a scatterplot showing the relationship between multiple-job rates in 2008 versus the latest unemployment data for December 2009. Each dot represents a state.
Positive relationship
Definition: A relationship between two variable in which, as the value of one variable increases the value of the other variable tends to increase also.
Example: http://www.zmag.org/znet/viewArticle/23718
Application: This article states that scholarly studies of Congress find a strong positive relationship between campaign contributions from interest groups and legislators’ voting on bills benefitting those groups. “While this relationship is not consistent for public policy issues that are of high salience and strongly contested, the relationship holds for low visibility issues – which account for the vast majority of bills passed.”
Negative relationship
Definition: A relationship between two variable in which, as the value of one variable increases, the value of the other variable tends to decrease.
Example: http://www.npr.org/templates/story/story.php?storyId=122984028
Application: In this article, researchers found a strong negative relationship between the amount of time that kids spend with media, such as television, the internet or texting, and the type of grades that they report getting.
No relationship
Definition: A relationship between two variable does not exist.
Example: http://blogs.suntimes.com/ebert/2010/01/a_superwoman_for_kenya_but_ame.html
Application: In the study in this article about the relationship between the wealth of schools and the performance of their students, the statistics find no relationship between such luxurious schools and test scores.
Linear relationship
Definition: A relationship between two variables that can be described by a straight line.
Application: While 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: "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 of r-squared indicating the common variance of variables X and Y.
Example: http://nejm.highwire.org/cgi/content/full/346/11/811
Application: "For the nuclear and the mitochondrial gene, respectively, 96 percent and 98 percent of the differences between duplicate measurements were less than 2 SD from the mean difference, with Pearson's correlation coefficients of 0.94 and 0.99 and coefficients of determination of 89 percent and 97 percent, respectively."
Correlation does not equal causation
Definition: A phrase used in science and statistics to emphasize that correlation between two variables does not automatically imply that one causes the other.
Example: http://www.vizworld.com/2010/03/correlation-imply-causation/
Application: "It bears repeating once again that Correlation does not imply Causation." In this article researchers show "the dueling charts that attempt to show one political party in the United States is better than another political party based on government statistics plotted against who is in power."
Extra-Credit (3 points each)
Normal Distribution
Definition: A theoretical mathematical distribution that specifies the relative frequency of a set of scores in a population.
Example: http://www.marxist.com/manifesto-students-education-cuts-socialist-alternative.htm
Application: "There is the example from the University of Hertfordshire of a post doc researcher required to give lectures. His duties involved some marking. After marking his students and giving appropriate feedback, the module leader edited his marking to fit what is termed ‘normal distribution’. Over a period of time some students saw an increase in the marks they received, yet a lowering of their grade as the module leader fiddled the grade-boundary in order to achieve ‘normal distribution’. Normal distributions are an abstract mean average, meaning that in reality we will have excellent students who are denied the best grade through no fault of their own, and also less competent students who have nevertheless been awarded a degree that does not match their ability."
Symmetrical
Definition: A frequency distribution that when folded at a midpoint produces two halves identical in shape.
Example:
Application:
Asymptotic
Definition: A distribution for which the tail of the distribution never touch the X axis.
Example:
Application:
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:
Application:
Sampling Error
Definition: The amount by which a sample mean differs from the population mean.
Example: http://edition.cnn.com/2010/POLITICS/02/22/broken.government.congress/
Application: A poll in this article found that 56 percent of those sampled said most Democrats in Congress do not deserve to be re-elected. An equal amount also said that most Republicans in congress don't deserve re-election. Thirty-four percent of those polled think most members of Congress should be re-elected, the lowest number recorded for that question in a CNN poll. The poll had a sampling error of plus or minus 3 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.americanchronicle.com/articles/yb/140953740
Application: Because of the lack of clear expectations about the relationship between strength of authority and financial condition on lending decisions, the researchers in this article propose a null hypothesis: There is no interaction between strength of authority and financial condition on lending decisions.
Alternative Hypothesis
Definition: A statement of what must be true if the null hypothesis of a statistical test is false.
Example:
Application:
Significance level
Definition: A probability value that provides the criterion for rejecting a null hypothesis in a statistical test.
Example:
Application:
Two-tailed test
Definition: A statistical test using rejection regions in both tails of the sampling distribution of the test statistic.
Example:
Application:
One-tailed test
Definition: A statistical test employing a rejection region in only one tail of the sampling distribution of the test statistic.
Example:
Application:
Degrees of Freedom
Definition: The number of scores free to vary when calculating a statistic.
Example:
Application:
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/716027
Application: Also in this study covered in 'random assignment,' the researchers assumed a type I error two-sided of 5%.
Type II Error
Definition: The error in statistical decision making that occurs if H0 is not rejected when it is false and the alternative hypothesis (H1) is true.
Example: http://psychservices.psychiatryonline.org/cgi/content/full/61/2/189
Application: A study where researchers studied patients from their first episode of psychosis before neuroleptic treatment and measured their adherence to medication at a later stage gave them an opportunity to identify risk factors from time of first presentation for future nonadherence. The results reproduced findings from other studies in terms relations between more symptoms, less insight, and negative attitudes toward treatment and nonadherence. However, they did not find that the variables at first presentation of psychosis predicted nonadherence four years later. The researchers believe that this is a result of a type II error.
Power
Definition: The probability of rejecting H0 when H0 is false and H1 is true. The power of a statistical test is given by 1 - beta.
Example: http://www.medscape.com/viewarticle/716027
Application: In this same study covered in 'random assignment,' the researchers determined that a sample size of 800 would provide 80% statistical power to detect a 30% reduction in the primary outcome from 30%.
Pairwise comparisons
Definition: Statistical comparisons involving two means.
Example:
Application:
Post-hoc comparisons
Definition: Statistical tests that make all possible pairwise comparisons after a statistically significant Fobs has occurred for the overall analysis of variance.
Example: http://www.aidsmap.com/en/news/6A449523-FE9A-4F11-8210-DC9D3B6339E1.asp
Application: In the study discussed in this article about Antiretroviral drugs having variable effects on bones and fat, the researchers found, in a post-hoc- comparison of the percentages of people who experienced a 20% or greater limb fat loss, that showed variation: 8.9%, 0%, 3.8% and 6.1%, respectively.
◄ Back to Winter 2010 - Inferential Statistics - PSY302 page
