Hw questions for quiz 5
rejection of a true null hypothesis (also known as a "false positive" finding or conclusion); also denoted as alpha
Type 1 Error
1. force entry/simultaneous 2. hierarchical 3. stepwise
Types of multiple regression
Independent t-test
UMW decide to see whether performance-related pay would improve moraleamongst their lavatory cleaners. Each month, twenty lavatory cleaners are paid on thebasis of the length of the bristles on their lavatory brush (on the assumption that theharder they have worked, the shorter their bristles will be). Another twenty are paid theirusual near-subsistence-level wages, regardless of how hard they work. After 6 months,each worker is asked to rate how happy they are in their job, using a 10 item job satisfaction scale.Which test would you use to see if performance-related pay has affected workers'morale?
Unit change in Y for each unit change in X (holding other IVs constant) Difficult to interpret because of different units ***Use to write regression equation
Unstandardized coefficients (b)
Predict an outcome (DV = Y) from multiple predictors (IVs = X)
Use a multiple regression when you want to...
the difference between a person's predicted score on the criterion variable and the person's actual score on the criterion variable.
error (in prediction)
one set of predictors used based on theory
forced entry or simultaneous regression
(x-mean)/standard deviation
z score equation
two IVs, but.. IV1 = independent groups (aka between-subjects) IV2 = repeated measures (aka within-subjects)
2 way mixed anova
chi-square test of independence
200 men and 150 women are asked to decide which one of the following features is most important to them when they choose a new car: price, performance, safety level, roominess, or color. Which test would you use to see if men and women differ in their preferences?
a main effect of the commercial
30 adults and 30 children were randomly assigned asked to view one television commercials for Burger King Whopper hamburgers and rate their interest in consuming the product. 10 adults and 10 children saw each of the following types of commercials: 1) humorous; 2) emotional; 3) factual. If you were to test if the type of commercial had an effect on desire for the product regardless of the age of the person watching, what would you be testing?
no
A botanist is interested in learning if different types of spring flower bulbs perform better in dry conditions vs. wet conditions. She experimented with 30 bulbs in each condition. Here is her data showing the mean height of the plants in centimeters at maturity. ..............Tulips.....Daffodils.....Bluebells Wet.........12.................12....................6 Dry..........16.................12....................2 Does there appear to be a main effect of condition (wet vs. dry)?
no
A botanist is interested in learning if different types of spring flower bulbs perform better in dry conditions vs. wet conditions. She experimented with 30 bulbs in each condition. Here is her data showing the mean height of the plants in centimeters at maturity. ..............Tulips.....Daffodils.....Bluebells Wet.........12.................12....................6 Dry..........16.................12....................2 If you had to run a simple effect on this data, does it appear that there would be a simple effect of condition @ daffodils?
yes
A botanist is interested in learning if different types of spring flower bulbs perform better in dry conditions vs. wet conditions. She experimented with 30 bulbs in each condition. Here is her data showing the mean height of the plants in centimeters at maturity. ..............Tulips.....Daffodils.....Bluebells Wet.........12.................12....................6 Dry..........16.................12....................2 Is there an interaction?
yes
A botanist is interested in learning if different types of spring flower bulbs perform better in dry conditions vs. wet conditions. She experimented with 30 bulbs in each condition. Here is her data showing the mean height of the plants in centimeters at maturity. ..............Tulips.....Daffodils.....Bluebells Wet.........12.................12....................6 Dry..........16.................12....................2 Does there appear to be a main effect of bulb type?
two way between groups ANOVA
A dentist randomly assigns people to use of three different forms of dental hygiene: 1) dental floss, 2) wooden toothpicks, or 3) anti-plaque rinse. After six months, she measures, in grams, how much plaque she scrapes off of the teeth. What statistical test should she use?
independent samples t-test
A research wants to replicate an earlier finding that those who watched Sesame Street as a child have higher GPAs in high school than those who did not. She divides students into 2 groups based on whether or not they watched Sesame Street and compares their GPAs. What test should she run to test the comparison?
two way between subjects ANOVA
A researcher investigates four different methods for coping with extreme stress. Each person attempts to assemble an IKEA flat-pack wardrobe (the stress-induction phase of the study), and is then allocated randomly to one of four groups. Those in the first group practice yoga for twenty minutes; those in the second group engage in deep breathing fora similar amount of time; those in the third group spend twenty minutes in a pub, drinking a pint of beer; and those in the fourth group simply scream at the top of their voice for twenty minutes. Each participant then provides a rating on a 0-10 scale of how stressed they feel. The researcher records the sex of each participant. Which test would you use to determine whether the four methods differ in their effectiveness for relieving stress and if the best method is different for men than it is for women?
correlation
A researcher is interested in factors affecting reproductive success based on wealth. She traps a hundred males from office buildings in D.C. and records the price of their suits. She then releases them back into the wild and follows them for a week, recording how many females each one mates with. Is there a relationship between wealth (as reflected in suit price) and reproductive success (as reflected in how many females each male mates
9
A researcher is interested in how perceptions of global warming influence consumer spending. He selects a sample of 10 environmentalists with strong perceptions of global warming and has them report how much they spend on typical items. The items were characterized as detrimental, safe, or helpful to the environment. Source................SS.......df......MS......F Item Type........396 Participants.....234 Error Total...................1278 How many df would this study have for participants?
36
A researcher is interested in how perceptions of global warming influence consumer spending. He selects a sample of 10 environmentalists with strong perceptions of global warming and has them report how much they spend on typical items. The items were characterized as detrimental, safe, or helpful to the environment. Source................SS.......df......MS......F Item Type........396 Participants.....234 Error Total...................1278 What is the MS for Error?
two way mixed ANOVA
A researcher wanted to find out if carbohydrate intake and number of hours of sleep had an effect on how long it takes people to run one mile. She randomly assigned people to either a low carb or a high carb diet the day of people to either a low carb or a high carb diet the day of each race. On three consecutive days, she had five people in each group vary the amount of sleep they got before a one mile run and recorded the number of before a one mile run and recorded the number of minutes it took to complete the run. Which test?
correlation
An experimenter wants to know whether experience affects how well shop-keepers can identify children who ask for cigarettes but are under the legal age for purchasing them. Each of 30 tobacconists is shown a random sequence of 40 photographs of young faces, and asked to decide whether each face is younger or older than the legal age for buying cigarettes. (Half of the faces are aged above the legal age, and half below). The experimenter records the number of correct decisions per participant, and also asks each shop-keeper how long they have been selling cigarettes (under 2 years or over 2 years). Which test should the experimenter use to decide whether experience leads to better age-estimation in this group?
chi-square
An instructor is interested if college men are more likely to turn their papers in late than college women. For each of her students she records whether their final paper was turned in late or not. Which test will tell her if "lateness" and sex are related?
comparing the pattern of cell means across one row to the pattern of cell means across another row
An interaction effect can be identified by
chi-squared
Are boys likely to pick violent video games more than girls? Boys and girls were given the opportunity to select one of three video games-a violent video game, a humorous video game, or a sports-related video game. Name that Test!
two-way between ANOVA
Assume that Dr. Kolar, who likes to do research on environmental issues ran his analysis and showed you his output. On his output was a source table that looked like this: Source....................................df Method of Education.......3 Type of Issue........................2 Method x Type...................6 Error.......................................148 What statistical test did Dr. Kolar ru sn?
ME consumer age, ME type of commercial, commercial type x consumer age, error
Assume these are the cell means (Average rating for each group on a 10 point rating scale) for the problem above: ...................Humorous....Emotional....Factual Children...........8........................4...................4 Adults...............4........................8...................4 Given the question above, the total variance would be made up of what "sources"?
Subtract the GM from the marginal mean of the streaming group they are in
Assume you are interested in satisfaction ratings of Netflix, Hulu, and Amazon Prime customers. You are also interested in knowing if the satisfaction rates of these streaming options differ based on whether you are young (under 25) or old (over 65). If you wanted to calculate the SS for the main effect of type of streaming device, how would you do it? For each person, I would start by...
1. The population of each variable (X and Y) follows a normal distribution 2. There is an equal distribution of each variable at each point of the other variable 3. the relationship between the two variables is linear (and not curvilinear) 4. the people (or cases) are independent
Assumptions for the Significance Test of a Correlation Coefficient
1. there is an equal distribution of each variable at each point of the other variable 2. the relationship between the variables is linear 3. the people (or cases) are independent 4. the error scores (that is, the difference between the prediction rule's predicted scores on the criterion variable and people's actual scores on the criterion variable) are normally distributed 5. both the predictor and the criterion variable are equal-interval numeric variables
Assumptions of multiple regression
1. Normal distribution of the DV in the population (robust if N >> 30) 2. Independence of observations WITHIN but NOT between groups 3. Homogeneity of variance 4. sphericity
Assumptions of one way RM ANOVA
1. Sample independence 2. Scores are normal distributed in population 3. Homogeneity of Variance 4. dependent variable should be continuous
Assumptions of one-way ANOVA
1. Normal distribution of the DV in the population (robust if N >> 30) 2. Independence of observations WITHIN but NOT between groups 3. Homogeneity of variance -less robust to violations -unequal n is more problematic 4. sphericity
Assumptions of two way RM ANOVA
1. Sample independence 2. Scores are normal distributed in population 3. Homogeneity of Variance 4. dependent variable should be continuous 5. two independent variables should be categorical, independent groups
Assumptions of two-way ANOVA
r = [Σ(ZxZy)] / N
Calculating correlation coefficient (conceptually)
a measure of effect size that assesses the difference between two means in terms of standard deviation, not standard error
Cohen's d
describes the relationship between two variables-- the usual measure describes the relationship between two equal-interval numeric variables
Correlation
1. number of predictor variables 2. because multiple predictors overlap in predicting the DV the standardized regression coefficient (β) for each predictor variable is not the same as the ordinary correlation coefficient (r) of that predictor with the criterion variable--both the standardized and the regular regression coefficients are about the unique, distinctive contribution of the variable, excluding any overlap with other predictor variables
Difference between a simple regression and a multiple regression?
In a simultaneous model, all IVs are treated simultaneously and on an equal footing. Such a research strategy is clearly most appropriate when we have no logical or theoretical basis for considering any variable to be prior to any other In a hierarchical regression model the IVs are entered cumulatively according to some specified hierarchy which is dictated in advance by the purpose and logic of the research
Difference between a simultaneous and hierarchical regression
The principle is that for any correlation between variables X and Y, there are at least three possible directions of causality: 1. X could be causing Y. 2. Y could be causing X. 3. Some third factor could be causing both X and Y.
Direction of causality
Independent samples t-test
Does anxiety affect sleep patterns? Dr. Stebbins measures the anxiety of 75 college students using the State-Trait anxiety scale. She selects the 20 students with the lowest anxiety scores and places them in one group(the low anxiety group). She selects 20 students with the highest anxiety scores and places them in another group (the high anxiety group). She compares these two groups on students on their self-reported hours of sleep for the previous week. What test would she run to make this comparison?
2 way between subjects ANOVA
Dr. Stahlman, our resident "rat runner", has two types of rats (20 brown rats and 20 white rats). He hypothesizes that brown rats learn faster than white rats when fruit loops are used as a reward, but that white rats learn faster than brown rats when Cocoa Puffs are the reward. Ten rats of each color are measured using Fruit Loops as a reward. The other rats are measured using Cocoa Puffs. The number of errors the rats make when learning the maze is recorded. What test should Dr. Stahlman run?
a simple way of quantifying the difference between two groups that has many advantages over the use of tests of statistical significance alone. Emphasizes the size of the difference rather than confounding this with sample size—The strength of the relationship between two variables on a numeric scale
Effect size
(y-ŷ) SSError = Error^2 = Σ(Y-Ŷ)^2
Error in regression is figured by
SSTotal = Σ(Y- Mean_of_Y)^2 VS. SSError = Error^2 = Σ(Y-Ŷ)^2
Error with mean vs error with regression
F = t^2
F test used to test regression model
MS/error
F-value equals
the probability of making one or more false discoveries, or type I errors when performing multiple hypotheses tests
Family-wise error rate
Recruit 20 subjects and test their blood pressure under all 3 different conditions
Harold wants to know if a new heart medication will lower blood pressure. He would like to test two doses of the new medication against a control. Which of the following ways of setting up the study would give him the most power?
The differences in ratings within each playing strategy
Here's a different study: A sample of 21 expert chess players rated the effectiveness of six different playing strategies. In the question above, what variance is included in the error term?
5, 100
Here's a different study: A sample of 21 expert chess players rated the effectiveness of six different playing strategies. What is the df for between groups and what is the df for error?
ordered set of predictors based on theory
Hierarchal regression
5 main differences! 1. IVs are interval/ratio level 2. can be nominal 3. question is about prediction 4. used in non-experimental research 5. less robust to violations of assumptions
How are regressions different from ANOVAs
160
How many people do you think were in this study? Source.....................................df Method of Education........3 Type of Issue.........................2 Method x Type....................6 Error.........................................148
Conduct simple effects
If an interaction in a 2 Way ANOVA is significant, what is your next step?
Conduct simple effects
If the interaction in a two-way design is significant, what is your next step?
the interaction of the two main effects in the study
In a one-way repeated measures design, what is used as the interaction term?
The variance within each cell
In a two-way between subjects ANOVA, what does the error represent?
The within subjects variance for the omnibus test
In any two-way ANOVA, what is the denominator for the F ratio for each main effect?
Two-way repeated measures
In one of the ANOVA models we looked at, each main effect and the interaction had its own error term. Which model was this?
Two-way between subjects ANOVA
In one study, people were randomly assigned either to come to class all the time, or to never come to class and to get the lecture notes from Canvas. Those who came to class were in the Lecture condition, while those who did not come to class were in the Distance Learning condition. The students were also divided according to their GPA prior to the class. There were people with Higher GPAs (over 3.0) and people with Lower GPAs (below 3.0). The students were compared on the total number of points they received in the class (out of 400 possible points). What statistical test do you think was run?
the dependent variable, represented by Y
In simple regression a criterion variable is
the independent variable, represented by X
In simple regression a predictor variable is
based on standard deviations (like z scores) so they can be compared compare sizes of beta ~ relative importance of predictors
Interpreting β for multiple regression
one-way repeated ANOVA
It's often said that you're hungry again soon after a Chinese meal. An experimenter puts this to the test. There are four conditions, and each participant does each one, on a different day of the week (order of conditions is counterbalanced across participants). In the first, participants eat an Indian takeaway; in the second, they eat a pizza; in the third, they eat a Chinese takeaway; and in the fourth, they eat a Kentucky Fried Chicken takeaway. All the meals are equated for bulk of contents and calorific value. The dependent variable is the loudness of each participants' stomach rumblings (in decibels), measured one hour after they have eaten the meal. These measurements are normally distributed. Which test should be used to decide whether there is a difference between these meals in terms of how quickly people get hungry again after eating them?
SS/df
MS equals
Ŷ= a + (b1)(X1) + (b2)(X2) + (b3)(X3) b1 to b3 = slope weights for each predictor X1 to X3 = the raw score on each predictor
Multiple regression equation
7.33, 7.00, 6.33
My brother, Mark, makes custom electric guitars. He uses all types of wood to create these guitars. Often the base of the guitar is made of different material and the finish of the guitar can include different types of lacquer. Let's say he has people rate the quality of sound they hear based on the type of wood type of lacquer finish. He gets the following mean ratings: ................Lacquer A....Lacquer B....Lacquer C Maple..........9........................6........................7 Ash...............7........................6.......................8 Hickory.......8........................4......................7 If in the omnibus test, the Main Effect of Type of Wood is significant, what three numbers does that test suggest are different from one another?
The 3 marginal means of type of Lacquer are not different from one another
My brother, Mark, makes custom electric guitars. He uses all types of wood to create these guitars. Often the base of the guitar is made of different material and the finish of the guitar can include different types of lacquer. Let's say he has people rate the quality of sound they hear based on the type of wood type of lacquer finish. He gets the following mean ratings: ................Lacquer A....Lacquer B....Lacquer C Maple..........9........................6........................7 Ash...............7........................6.......................8 Hickory.......8........................4......................7 Let's assume we run SPSS and get a sig value for the main effect of lacquer of .48. What does that mean?
9.00, 6.00, 7.00
My brother, Mark, makes custom electric guitars. He uses all types of wood to create these guitars. Often the base of the guitar is made of different material and the finish of the guitar can include different types of lacquer. Let's say he has people rate the quality of sound they hear based on the type of wood type of lacquer finish. He gets the following mean ratings: ................Lacquer A....Lacquer B....Lacquer C Maple..........9........................6........................7 Ash...............7........................6.......................8 Hickory.......8........................4......................7 Using this data, if you were to test the simple effect of Lacquer Type at Maple, what means would you be comparing?
Test just one set of the simple effects to determine why the interaction is signficant
My brother, Mark, makes custom electric guitars. He uses all types of wood to create these guitars. Often the base of the guitar is made of different material and the finish of the guitar can include different types of lacquer. Let's say he has people rate the quality of sound they hear based on the type of wood type of lacquer finish. He gets the following mean ratings: ................Lacquer A....Lacquer B....Lacquer C Maple..........9........................6........................7 Ash...............7........................6.......................8 Hickory.......8........................4......................7 If Mark found that the interaction between type of wood and type of finish was significant, what would be his next step?
chi-square
NAME THAT TEST! Imagine you surveyed a group of people and asked them the following questions: 1) What sex do you identify as? 2) Do you smoke cigarettes? You want to know if there is a relationship between sex and smoking. What test would you run?
the probability that the test rejects the null hypothesis (H0) when a specific alternative hypothesis (H1) is true
Power
beta; the probability of making a type 2 error
Power is inversely related to
199
Previous research has found that we are better at recognizing faces of our own race compared to those of other races. This effect is known as 'Own-Race Bias' in face recognition. Imagine that you wanted to investigate whether this own-race recognition advantage exists for Asian and Caucasian adults. You could show participants of both races images of faces that are both Asian and Caucasian. (In other words, each participants sees both Asian and Caucasian faces). After a short break, you could then show them a larger pool of faces and ask participants to identify whether or not they had seen them before. In this example, there are two independent variables: 1) Race of Participant which has two levels: Asian and Caucasian. 2) Face Race also with two levels: Asian and Caucasian. The number of faces participants correctly recognize could be taken as the dependent variable. Assume that you have 50 Asian participants and 50 Caucasian participants in your study. What would be your total degrees of freedom for this study?
PROS: 1. more power to reject null 2. require fewer participants 3. less variability among participants -Can directly assess individual differences and subtract them out of error term -F is larger CONS: 1. more vulnerable to weak research design (i.e. threats to internal validity) -less robust to violations 2. order effects
Pros & cons of repeated measures design
-Isolate the effects of each X variable on the Y -improve degree of explanation of dependent (Y) variables Used when ... -explanation of variance is high - F-ratio and t-statistics are highly statistically significant
Purpose of multiple regression
two way mixed ANOVA
Some TV viewers in England complain to the BBC that Jeremy Clarkson's programme "Top Gear" is a bad influence on young drivers, given that it extols the virtues of speeding while driving. To determine whether there is any foundation to these claims, a researcher uses a speed camera to measure the speeds of 400 drivers on an A-road, the morning before the programme is transmitted. He follows this procedure again, the morning afterwards. Each car is photographed, so that the experimenter can select only those drivers who travelled that route on both occasions, and hence whose speeds were measured twice. The selected drivers were then contacted and asked whether or not they had watched "Top Gear" that week. Which test would you use to see whether drivers who watched "Top Gear" drove faster the following morning than drivers who did not watch it?
Two way mixed ANOVA (Participants: 10, conditions: 3)
Source.........................................................df.....SS...MS..F..Fcrit Btwn subjects IV1...................................................................1 error (IV1 X p's).........................................8 Within subjects IV2..................................................................2 interaction(IV2 X IV2)................................16 Interaction err (IV1 X IV2 X p's)........2 total............................................................29
two way within(RM) subjects ANOVA Participants (24) conditions: 4
Source................................................DF Paticipants (P's)................................5 Grade level........................................1 error (grade X p's).....................5 Lesson Type.......................................1 error (lessons X p's)..................5 Interaction (grade X lesson).......1 error (grade X lesson X p's).........5 Total........................................................23
two way between subjects ANOVA Participants: 10
Source..............................................df Btwn .......IV1................................................1 .......IV2...............................................1 .......Interaction (IV1 X IV2)........1 Within (error)................................6 Total.................................................9
One way within(RM) subjects ANOVA (60 participants)
Source.......................................df IV (condition)............................2 Participants...............................19 Error (Interaction; CxP)......38 Total............................................59
One way within(RM) subjects ANOVA Participants: 30
Source............................df IV (ex: level)..................2 Participants...................9 Error (level X p's).......18 total................................29
One way between subjects ANOVA participants: 30
Source.............SS...........df.........MS......F Between..........................2 Within...............................27 Total.................................29
the correlations among the levels of the variable in the population are equal the accuracy of the F test for repeated measures analysis of variance can be strongly affected by violations of this assumption.
Sphericity
For each person: X-GM = (X-M) + (M-GM) For Everyone Together: SSTotal = SSError +SSBetween
Structural model for one way ANOVA
(X-GM) = (X-Mcell)+(Mrow-GM)+(Mcolum-GM)+Interaction translation: Total variance= within(error) + main effect 1 + main effect 2 + interaction *interaction Effect: Total variance minus the other three deviations--> usually what solving for
Structural model in Two-way ANOVA
Correlation
Suppose a health psychologist tests if mood and eating are related by recording data for each variable for a sample of 45 participants. She measures mood with a 9 point rating scale and measures eating by the number of daily calories eaten. Name that Test!
Neither variable becuase there are not enough levels to be concerned
Suppose you conduct a study investigating the impact of an intervention on participants' depression symptoms (using pre-test and post-test design), but also investigating whether the impact varies for age (teenagers, middle-aged adults, elderly adults). You recruit 20 people from each age group, perform the intervention on the age groups, and measure their depression symptoms over time (Time 1 = pre-intervention and Time 2 = after the intervention). In the question above, which variable would you need to check to make sure it meets the sphericity assumption?
Age x time x participant
Suppose you conduct a study investigating the impact of an intervention on participants' depression symptoms (using pre-test and post-test design), but also investigating whether the impact varies for age (teenagers, middle-aged adults, elderly adults). You recruit 20 people from each age group, perform the intervention on the age groups, and measure their depression symptoms over time (Time 1 = pre-intervention and Time 2 = after the intervention). Create a source table for this problem and use it to answer the following questions. What would be used as the error term for the time of measurement test?
one way independent measures ANOVA
The local Fredericksburg ale, "Fred Red", is reputed to be imbued with truly magical medicinal properties that increase physical stamina. To investigate its effects, a researcher asks four groups of cyclists to cycle up a part of the Blue Ridge Parkway. One group drinks no Fred Red beforehand; another group drink one pint each; a third group drink two pints each; and a fourth group drink four pints each. The dependent variable is how fast each cyclist gets from the bottom of the mountain to the top. Which test would you use to see if drinking Fred Red affects the cyclists' speed of ascent?
Between subjects variance
Variance due to the race of the participant would be part of:
variance due to difference between participants in the study
What is subtracted out to make a smaller error term in a repeated measures design?
(x-M)
Which of the following represents error in an ANOVA (if you squared it?)
Cohen's d
Which of the following would you associate with a t-test?
It mixes a between subjects variable and a within subjects variable
Why is a mixed ANOVA called "mixed?"
to reduce the chances of obtaining false-positive results (type I errors) when multiple pair wise tests are performed on a single set of data. Put simply, the probability of identifying at least one significant result due to chance increases as more hypotheses are tested
Why use a bonferroni correction?
the number of standard deviations that a score is from the mean. Whatever the range of values of the variable, if you change your raw scores to high raw score = positive; low raw = negative -a very standard way just how high or low each score is in relation to the mean Pro: directly comparable from one variable to another always range between -1 and +1
Z-score
The significance level, also denoted α, is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference
alpha
1. data measured on a continuous/ordinal scale 2. data is collected from a representative, randomly selected portion of the total population 3. Scores are normal distributed in the population 4. reasonably large sample size used 5. homogeneity of variance
assumptions of independent samples t-test
the probability of Type II error in any hypothesis test-incorrectly concluding no statistical significance
beta
measure of degree of linear correlation between two variables ranging from −1 (a perfect negative linear correlation) through 0 (no correlation) to +1 (a perfect positive correlation) denoted by r +/- indicates direction, sum indicates strength -can determine significance by converting to a t value and comparing to cutoff scores on t table
correlation coefficient, also called Pearson's correlation coefficient
the result of multiplying a person's Z score on one variable by the person's Z score on another variable Σ(ZxZy) = sum of cross products
cross-product of Z scores
conduct a second multiple regression analysis using only the significant predictors ~ a reduced model
if only some variables in a multiple regression analysis are found significant, what should you do next?
the point where the regression line crosses the vertical axis; the regression constant (a).
intercept
the correlation between the criterion variable and all the predictor variables taken together, symbolized by R
multiple correlation coefficient
An interaction effect in a two-way factorial design
occurs when the influence of one variable that divides the groups changes according to the level of the other variable that divides the groups.
1 - Beta
power equals
Simply put: how much better is using regression line than the mean? --denoted by r^2 Calculate how much error is reduced-- [ (SStotal-SSerror)/SStotal ] where SSTotal = Σ(Y- Mean_of_Y)^2
proportionate reduction of error (PRE)
% of variance in this sample
reading SPSS: R square
% of variance in the population
reading SPSS: adjusted R square
run without predictors that were not significant to get best linear combination of variables to predict the outcome of interest
reduced model
are estimates of the unknown population parameters and describe the relationship between a predictor variable and the response(outcome variable) is typically a standardized regression coefficient (the slope of a line in a regression equation) used when both the criterion and predictor variables are standardized (i.e. converted to z-scores). ... If the independent/dependent variables are not standardized, they are called B weights
regression coefficients [beta (β) weights]
predict Y, given a known score on X
regression line (line of best fit)
The steepness of the angle of a regression line
slope
r^2, gives the proportionate reduction in error or proportion of variance accounted for in the criterion variable by all the predictor variables taken together. For example, an R of .40 gives an r^2 of .16, which means that the predictor variables together account for 16% (.40×.40 = .16, which is the same as 16%) of the variation in the scores in the criterion variable. R^2 is a measure of the effect size for multiple regression
squared multiple correlation coefficient
Change in X of one SD yields an increase in Y by β*SDy (holding other IVs constant) -For example, a standardized regression coefficient of .63 would mean for every increase of 1 standard deviation on X, we predict an increase of .63 standard deviations on Y. ***Used to compare the relative importance of various predictors in the model (some say you shouldn't)
standardized coefficient (β)
the likelihood that a relationship between two or more variables is caused by something other than chance
statistical significance
computer orders predictors
stepwise regression
must be greater that .05; p > .05
to meet the assumption of sphericity p must be
the failure to reject a false null hypothesis (also known as a "false negative" finding or conclusion); also denoted as beta
type 2 error
