# PSY302-300541142

### 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.nature.com/ejcn/journal/v56/n2/full/1601298a.html

Application: Two-sample t-test test the relationship betwwen a categorical variable and a continuous independet variable, in which the categorical independent variable is a between-subject design with two levels. The example measures the "effects of flaxseed supplementation as a part of daily diet on serum lipids, fatty acids and plasma enterolactone."

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.highbeam.com/doc/1G1-81017991.html

Application: The Two-sample t-test measures the relationship between a categorical and independent variable. In my example the t-test was used to measure of the analyses of coveriance I, coveraince II and general equations in their respond during a follow up.

## 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.dentistryiq.com/index/display/news-display/1194715688.html

Application: The one way Anova test the relationship between a categorical independent variable and a continues independent variable. In my example the study focuses on the differences between the ages of the participans who were treated with different types of Fs. They measured the differences among the four different sealants and determine which group or groups was responsible for any differences in the retention , marginal integrity and presence.

## Two-Way ANOVA test

Definition: Testing the relationship between two categorical independent variable and a continuous independent variable.

Example:http://www.biodieselmagazine.com/article.jsp?article_id=4203

Application: A Two-way Anova test the relationship between two categorical independent variable and a continuos independeble variable. In my example, the study focuse in the relationship between the data consisted of daily mileage driven and fuel consumption with the consideration to the route selection, driver assigment, and field data collection.Then All four data sets—two for B20 (express and stop/go), and two for ULSD (express and stop/go) with the Two-way Anova test to see if there was a significan difference.

## Correlation test

Definition: Testing the relationship between two continuous variables, either of which can be considered the independent or dependent variable.

Example:http://www.medscape.com/viewarticle/722163

Application: Correlation test the relationship between two continuous variable which can be considerein dependent or independent. I my exmaple they measure they measure the relationship between the total cost, intensive care at the end of life, and ambulatory medaica care. They found a negative relationship between the variables." Higher PSA screening in a region was positively associated with greater total costs (correlation coefficient (r)=0.49, P<.001), greater intensive care unit use at the end of life (r=0.46, P<.001), and greater number of unique physicians seen (r=0.36, P<.001). PSA screening was negatively associated with proportion of beneficiaries using a primary care physician as opposed to a medical subspecialist for the predominance of ambulatory care (r=−0.38, P<.001)."

## Chi-square test

Definition: Testing the relationship between two categorical variables, either of which can be considered the independent or dependent variable.

Application: Chi-square test for a relationship between teo categorical variable. In my example Chi-square measures "assigment of patients in a comparative clinical trial to the tentatively better treatment. However, due to the adaptation in patient allocation, the samples to be compared are no longer independent."

# Concepts

## Standard Score

Definition: A score obtain by using the ransformation z=(X-X bar)/S

Application: A standard score in the example is measuring the levels in the students basic math and communications level how they level to proficiency levels for garduation.

## Confidence Interval

Definition: A range of scoreds values expected to contain the value of mu with a certain level of confidence.

Example: http://www.indiablooms.com/LifestyleDetailsPage/lifestyleDetails270410a.php

Application: Confidence interval contains the level of confidence within a given event. In my example,tries to explain provocative dress didn't really seem to effect the frequency of earthquakes. There were 47 earthquakes on the 26th, which falls well within the 95% confidence interval for number of earthquakes" The confidence interval communicate that earthquakes occur due to natural forces and not because of provocative wear by women.

## Parametric Test

Definition: A Statistical test involving hypotheses that state a relationship about a population parameter.

Example:

Application:

## Nonparametric Test

Definition: A statistical test involving hypothesis that do not state a relationship about a population parameter.Also known as a distribution-free test.

Application: A nonparametric test involves a hypothesis that do not state a relationship abaout a population. In the example, the nonparametric test is used to measure, "All patients received perioperative prophylactic antibiotics. Surgical site infections were identified postoperatively, and defined using the Centers for Disease Control (CDC) criteria. Clinical parameters, comorbidities, smoking history and preoperative urine analysis and culture results were analyzed as well as operative data."

## Statistically significant difference

Definition:The observed value of the test statistic falls into a rejection region and H0 is rejected.

Example:http://www.dentistryiq.com/index/display/news-display/1194715688.html

Application: There were statistically significant differences between FSs for retention criteria at all follow-up examinations , and the difference was found to be due to the low retention rate of the DS group (Table 2). The observe value of the test statitic fell into the rejection region.

## Nonsignificant difference

Definition: The observe value of the test statistic does not fall into a rejection region and the null hypothesis is not rejected.

Example:http://www.dentistryiq.com/index/display/news-display/1194715688.html

Application:
The differences between FS with respect to both marginal integrityand presence of caries were not statistically significant at any follow-up examination. The le value servable value in the marginal integrityand did not fall into the rejection region therefore the null hupothesis was not rejected.

## Between-subjects Design, with two groups

Definition:An experiment in which two or more groups are created

Example: http://www.nature.com/clpt/journal/v84/n2/full/clpt200830a.html

Application: The experiment in which two or more groups were created. In the exampe.They, "manipulated “intrinsic” quit motivation by recruiting smokers who either did intend to quit soon (“treatment seekers,” N = 47) or did not (“nonseekers,” N = 93), and “extrinsic” quit motivation by providing or not providing reinforcement for abstinence ($12/day)."

## Between-subjects Design, with three or more groups

Definition:An experiment in which three or more groups are created.

Example:http://www.nature.com/sc/journal/v43/n9/full/3101756a.html

Application: In the experiment three or more groups were created measure, "leg kinematics and motion characteristics within able-bodied (AB) and spinal cord injured (SCI) individuals during stationary semireclined cycling."

## Random sampling

Definition: A sampling method in which individuals are selected so that each memeber of the population has an equal chance of being selected for the sample, and the selection of one memeber is independent of any other member of the population.

Application: In China the contaminated milk scandal has seen 53,000 babies in ill and killing four. The European Union has moved to ban imports of dairy-based Chinese food products, including biscuits, sweets and chocolate, aimed at children or infants amid the growing global health scare. New "precautionary" restrictions imposed by the European Commission will come into force on Friday along with tighter EU border checks on all Chinese food products entering Europe. But the Tesco supermarket chain has already removed Chinese-made White Rabbit Creamy Candies off shelves amid reports that samples of the product in Singapore and New Zealand had tested positive for melamine. New tests will be carried out on all imported goods from China containing more than 50 per cent of milk powder and random sampling will now be carried out on all such products already on the EU market and supermarket shelves.

## Random Assignment

Definition: A method of assigning subjects to treatment groups so that any individual selected for the experiment has an equal probobility of assgnment to any of the group and the assigment of one subject to a group does not affect the assignment of any other ndividual to that same group.

Example: http://www.mathematica-mpr.com/PDFs/randomassign.pdf

Application: random assigment was used to pick teachers, classrooms, or schools to use in the experiment. They were placed in a ramdom order to have a equal probability of the assigment.

## Independent Variable

Definition: A variable manipulation in an experiment to determine its effect on the dependent variable.

Example: http://www.nature.com/ijo/journal/v30/n2/full/0803053a.html

Application: An independent variable is variable use to manipulate in the experiment. In the example, nut chewing is used to measure obesity.

## 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 diffferent levels.

Example:

Application:

## Confounds

Definition: An extraneous variable that is covarying with the ondependent variable, potentially masking te true effect of the independent variable on the dependent variable.

Example: http://www.iwh.on.ca/confounding-variables

Application: A confound variable is a extreneous variable that covarying with the dependable variable. In the exaple,"two groups of workers — who were employed in different lumberyards — didn't do the same amount of heavy lifting. One lumberyard typically used forklifts to load and deliver orders by truck, while the workers at the other location were sometimes expected to load orders into the customers' vehicles. So this variable — the amount of lifting — rather than back belt use could explain the different rates of back strain in the two groups." This mistake mask the true effect of the independent variable on the dependent variable.

## Dependent Variable

Definition: The variable in an experiment that depends on the independent variable. in most instance the dependent variable is some measure of behavior.

Example: http://www.nature.com/ki/journal/v56/n4/full/4491047a.html

Application:
A dependable variable is a measurement of behavior. In the example, they measure calcitriol levels and BsmI genotype frequencies to determine,"Vitamin D receptor genotype influences PTH and calcitriol levels in predialysis patients."

## Within-subjects Design, with two groups

Definition: A research design in which two 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 repeated measures design or a treatment-by-subjects design.

Example: http://news.yahoo.com/s/ap/20100225/ap_on_re_us/us_abortion_fetal_pain

Application: A within-subject desig, within two groups was used to measure two groups(one for abortion and one against abortion) that will undergo the lecture explaining that the fetus does not feel pain after 20 weeks of pregnancy, to be able get their view on whether the bill should pass prohibiting abortions after this time period. They receive the answers, have the same groups listen to the next lecture discussing how the fetus does feel pain after 20 weeks of pregnancy and see if their veiws change on if the bill should pass or not.

## 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 reveices each treatment vondition. Also known as a repeated measures design or a treatment-by-subjects design.

Example:

Application:

## Main effect

Definition:The mean of all subjects given one level of an independent variable, ignoring the classification by the other independent variable in a factorial design

Application: Based on the average means you receive on determining which factor individually or combined, in reference to living in a natural or not natural habitat for the orca whale and receiving healthcare or not receiving healthcare. Determine which aspect of each factor has a higher impact on the orca whale.

## Interaction

Definition:A situation in a factorial design in ehich the effect of one independent variable depends on the level of the other independent variable with which it is combined.

Example: http://www.highbeam.com/doc/1P3-1707302391.html

Application: The experiment measures the effectpossible interaction between postural risk factors and job strain on the incidence proportion of self-reported musculoskeletal symptoms in the regions of the shoulder-neck, lower back, and upper limbs.

## Strength of Effect (Eta squared)

Definition: Is a measuremtn of how much knowing the level of an indepedent variable that a subject received reduceds the error in predicting the subject's score in the sample tested.

Example: http://www.highbeam.com/doc/1G1-180029905.html

Application: Eta square measure effect size. In the example," The overall effect size was trivial (r = 0.04). Interestingly, neither intervention program-based increases in physical activity nor dietary improvement was a significant moderator of effect sizes for BMI change. This suggested that improvements beyond the boundaries of structured programs are important."

## Scatterplot

Definition: A plot of a bivariate distribution in which the X variable is pltted on the horizontal axis and the Y variable is plotted on the vertical axis.

Application: We could graph the differences between the longevity of a whale in a natural habitat and those living in the theme parks based on how healthy they are.

## 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.highbeam.com/doc/1G1-119740230.html

Application: In a positive relationship the value of one variable tends to increase the value of the other. In the example, there is statistically significant evidence of a positive relationship between market volatility and the equity premium. When market volativity goes up, does the equity premium.

## Negative relationship

Definition:A relationship between two variables in which, as the value of one variable ncreases, the vale of teh other variable tends to decrease.

Example:http://www.highbeam.com/doc/1G1-126683358.html

Application:
A negative relationship between two variables one variable decreases while the other tends to increase. In the example, between anxiety and couse performance. As anxiety is reduce course performance goes up.

## No relationship

Definition: A relationship between two variables in which there is no relationship between them.

Example: http://www.nature.com/jhh/journal/v16/n8/full/1001452a.html

Application: there is no consistent relationship between blood pressure and blood lead in the NHANES III dataset.

## Linear relationship

Definition:A relationship between two variables such that each time variable X changes by one unit, variable Y changes by a constant amount.

Application: a lienear relationship is a relationship between two variables such that each time variable x chages by one unit. In the example,they addressed the question, whether there is a linear relationship between disability status and health related quality of life (HRQOL) in MS. They determine there was not a liners relatihip between the both because their was no change between the variables.

## Curvilinear relationship

Definition: A relationship between two or more variables which is depicted graphically by anything other than a straight line. For example an accelerating rate of increase in deaths with age is represented by a steepening curve. Curvilinear relationships are very variable, and more complex and less easily identified than simple linear relationships.

Application: this paper, we provide one explanation for the curvilinear relationship between crime and tem-perature by using the maximizing utility theory for offenders. In our model we show the possibilitythat the relationship would be linear when the cost for captured is small enough, and would be cur-vilinear when the cost is large

## Coefficient of Determination

Definition: The Value of r2 indicating the common variance of variables X and Y.

Example:http://agron.scijournals.org/cgi/content/abstract/65/3/459

Application: The value of r2 indicating the common varaince x and y. In the example is the relationship of radiation and partial leaf area indices (LAI's) to corn yields.

## Correlation does not equal causation

Definition:

Example:http://economix.blogs.nytimes.com/2010/04/12/do-smarter-workers-work-less/

Application: In the chart below, Mr. Florida, director of the Martin Prosperity Institute at the University of Toronto, plotted states according to human capital — here defined as what share of their work force had at least a bachelor’s degree — and how much their average worker earned per hour. As you can see, states with more college graduates tended to have higher wages (with a correlation of 0.65). And that’s not all. He also looked at the relationship between human capital and hours worked. Generally speaking, states with more highly educated workers worked shorter weeks (with a correlation of negative 0.59). Of course, correlation is not causation. But plenty of research indicates that a more educated local economy is a healthier economy, as one of our Daily Economists, Edward L. Glaeser, has written. So it does not seem such a stretch to find a pattern between human capital and earnings or more convenient hours.

# Extra-Credit (3 points each)

## Normal Distribution

Normal Distribution: A theoretical mathematical distribution that specifies the relative frequency of a set of scores in a population.

http://www.opposingviews.com/i/measuring-nfl-defensive-playmakers

The relative frequent distribution of player's individual performance from play to play almost certainly follows a normal distribution. Virtually all aspects of human traits and performance are governed by a bell curve, from height to intelligence to athletic feats.

## Symmetrical

Symmetrical distribution: A freqquency distribution that when folded at a midpoint produces two halves identical shape.

http://www.opposingviews.com/i/measuring-nfl-defensive-playmakers

The distribution of an athlete's performance is roughly symmetric with respect to his own mean performance level. The frequency distribution midpoint halfs are identical in shape.Event though, Nearly all sports statistics are based in some way on the normal distribution, and each player's performance on individual plays is unlikely to be an exception

## Asymptotic

http://www.istockanalyst.com/article/viewarticle/articleid/4056256

The problem with paying them is that the problem(s) that caused the maintenance call has not gone away, so new maintenance calls are likely... and you have only so much cash. Sadly, if you instead liquidate, you must sell many more times the amount of the call just to meet the call, which effort rapidly becomes asymptotic; the two data points only seem to converge.

## Continuous

Continuous: A variable that can take on an infinite set of values between the limits of the variable.

http://www.inforum.com/event/article/id/277249/group/News/

Continuous tornado damage paths in excess of 100 miles are unusual, but do happen on occasion.

## Sampling Error

http://thecaucus.blogs.nytimes.com/2010/05/03/new-poll-economic-uplift/

The nationwide telephone poll was conducted April 28 to May 2 with 1,079 adults and has a margin of sampling error of plus or minus three percentage points. More results from this survey will be available after 6:30 p.m.

## Null Hypothesis

The null hypothesis has not been disproven; according to the best science currently available there is no correlation between vaccines and autism, and FRONTLINE was correct to hammer that point home again and again.

## Alternative Hypothesis

http://www.indiablooms.com/LifestyleDetailsPage/lifestyleDetails270410a.php

“As per the USGS Earthquake website data, not only did all of the earthquakes on boobquake fall within the normal range of magnitudes, but that mean magnitude actually decreased slightly!” “Now, this change isn't statistically significant, but it certainly doesn't support the cleric's claim. In fact, I think it develops an even more interesting alternative hypothesis: Maybe immodest women actually decrease the amount of earthquakes!”

## Significance level

http://economix.blogs.nytimes.com/2009/08/12/does-higher-unemployment-lead-to-more-drug-use

Mr. Florida took a look at how health and happiness correlated with drug use. Before he did so, I told him I guessed healthier and happier states used fewer drugs; his hunch was the opposite. Turns out we were both wrong. When he ran the numbers using the Gallup-Healthways Well-Being Index and its sub-components (which include measures of health), there were no significant relationships, he /said.

## Two-tailed test

## One-tailed test

## Degrees of Freedom

http://www.leagle.com/unsecure/page.htm?shortname=infco20100413161

The field of invention is hand-operated controllers for the movement of images on a computer screen or television display, particularly as used in video games. The controller is the tool by which human hands manipulate a graphic image, a procedure called "hand inputs." The hand inputs are implemented through handles such as joysticks or trackballs, whereby the hand actions of the human operator are sensed and translated electronically into corresponding linear and rotational movements that are shown in graphic display. As discussed in the patents in suit, hand inputs move images in six general directions that are called "degrees of freedom" (DOF) in the lexicon of this technology. Thus, the hand inputs may produce linear movement along three axes (forward/backward, left/right, or up/down), and rotational movement about the three linear axes (roll, pitch, or yaw).

## Type I Error

Imagine that you are a hominid on the planes of Africa and you hear a rustle in the grass. Is it a dangerous predator or just the wind? If you assume the rustle in the grass is a dangerous predator and it is just the wind, you have made a Type I error (a false positive), but to no harm. But if you believe the rustle is just the wind when it is a dangerous predator, you have made a Type II error (a false negative) and there's a good chance you'll be lunch and thereby removed from your species' gene pool. Because we are poor at discriminating between false positives and false negatives, and because the cost of making a Type I error is much lower than making a Type II error, there was a natural selection for those hominids who tended to believe that all patterns are real and potentially dangerous. This is the basis for the belief not only in God, but in souls, spirits, ghosts, demons, angels, intelligent designers and all manner of invisible agents intending to harm us or help us.

## Type II Error

Imagine that you are a hominid on the planes of Africa and you hear a rustle in the grass. Is it a dangerous predator or just the wind? If you assume the rustle in the grass is a dangerous predator and it is just the wind, you have made a Type I error (a false positive), but to no harm. But if you believe the rustle is just the wind when it is a dangerous predator, you have made a Type II error (a false negative) and there's a good chance you'll be lunch and thereby removed from your species' gene pool. Because we are poor at discriminating between false positives and false negatives, and because the cost of making a Type I error is much lower than making a Type II error, there was a natural selection for those hominids who tended to believe that all patterns are real and potentially dangerous. This is the basis for the belief not only in God, but in souls, spirits, ghosts, demons, angels, intelligent designers and all manner of invisible agents intending to harm us or help us.

## Power

## Pairwise comparisons

## Post-hoc comparisons

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