FINAL STUDY FOR IS
What are the elements of a dependent group design?
A repeated-measures design is one in which the dependent variable is measured two or more times for each individual in a single sample. The same group of participants is used in all treatment conditions. The repeated-measures design differs from a between-measures design because it has only one group of participants whereas the between-measures design has two or more groups of participants.
What is an interaction?
"extra" mean differences that are not explained by the main effects - for example, combinations of self-esteem and audience levels acting together - separate from main effects When the two factors are not independent, so that the effect of one factor depends on the other
What is the difference with Tukey's Post Hoc Test and t-test for two independent samples?
you should be concerned about the experimentwise alpha level because for each pairwise comparison, you perform a series of hypothesis test the problem is fixed by using the Tukey's HSD test because you use only one alpha level for one hypothesis test - it is within the same experiment-wise error (MS within) - For the two independent samples either t or f can be used as they always result in the same decision
The least-square regression line. Why does this line "best" describe the data?
- For each value of X in the data, this equation determines the point on the line (Y - Yˆ) that gives the best prediction of Y. - minimizes the error between the actual data point (Y) and the predicted point on the line (Y^) - (1) get this line by obtaining the difference in the distance (Y-Y^), then (2) squaring each and adding them up to obtain the measure of the overall squared error between the line and data, (3) from there you can define the best-fitting line as the one that has the smallest total squared error. Basically, the least-square regression line minimizes the error between the actual data point and the predicted point on the line by defining the best-fitting line as the one that has the smallest total squared error.
What is the relationship between ANOVA and t-test?
1. F = t squared - t-statistic compares distances between two sample means and distance computed for standard error. in F-ratios, variance is a measure of squared distances 2. the two tests always reach the same conclusion about the null hypothesis 3. the df for the t-statistic is the same in the denominator of the F-ratio 4. the t-distribution matches perfectly with the F-distribution due to F = t squared - any value in the critical region for t ends up in the critical region for F after it is squared
What are the assumptions for regressions?
1. Independence of observations between the participants - each score of a participant should be independent of all other participants' scores 2. Bivariate normality (simple) or multivariate (multiple) - each of the variables should be normally distributed on its own and for any value of one variable, the scores on the other variable should also be normally distributed 3. Homoscedasticity - variances on the dependent variable are equal in the population for all levels of the independent variable. Mild to moderate violations of this assumption is generally tolerable.
What are the conceptual steps of hypothesis testing?
1. State the hypothesis about a population. - null hypothesis - alternative hypothesis 2. Predict the characteristics of the sample based on the hypothesis. 3. Obtain a random sample from the population. 4. Compare the sample data with the prediction made from the hypothesis. - If the data is consistent with the prediction, we can conclude that the hypothesis is reasonable and "fail to reject the null". - If the data is discrepant, we reject the null hypothesis.
What are the advantages and disadvantages of a dependent group design?
ADVANTAGES - requires fewer participants - well suited to show any changes that occur over time (e.g. treatment effect; behavioral changes) - results no longer bias by reducing and eliminating individual differences. Omits the risk that participants in one treatment are substantially different from participants in the other treatment - in between-measures design, theres a chance participants in one sample are systemically different from the other participants DISADVANTAGES Time-related effects - change in a person's emotional well-being between treatments, or health - weather changes Order Effects - participants second score was influenced by the test in the first condition rather than the treatment - e.g. they get better at an IQ test through practice rather than studying (practice effect) Counterbalancing - helps get rid of possible order effects and time-related effects - one group of the participants does treatment 1 and 2 in that order. The second group does treatment 2 and 1 in that order. - The goal of counterbalancing is to distribute any outside effects evenly over the two treatments
What are the advantages and disadvantages of an independent groups design?
Advantages - no gap in time (error from time eliminated) - one time study (quick) - can have more than two groups/treatment conditions to increase chances of significance Disadvantages - differences between random sampling - can either deals with individual differences within groups or differences due to treatment effects
What is the relationship among the alpha, power, and beta?
As the alpha level decreases, the power decreases and the same occurs when the values increase As the power increases, beta gets smaller and vice versa
Why a nonparametric test is called a distribution free test?
Do not state hypotheses in terms of parameter and only meet few (if any) assumptions
What factors can affect the variability among scores?
BT variance = treatment effects + unsystematic, random factors - general differences between treatments - sampling error WT variance = unsystematic, random factors - individual differences within each treatment Larger numerator = larger F-value Larger denominator = smaller F-value
What is the between-measures? What is the repeated-measures? Differences in analysis?
Between-measures measures three or more different groups of participants in each condition Repeated-measures measures the same group of participants over time in three or more different conditions - design automatically removes individual differences in numerator, and subtracts IDs from the denominator
What are the elements of an independent groups design?
Between-subjects research design - uses separate group of participants for each treatment condition (or for each population) - one independent variable
What is the relation between the population mean and the mean of the sampling distribution of the mean?
Expected value of M: the mean of the sampling distribution of the mean is equal to the mean of the population of scores The distribution should be normal
What is the central limit theorem? What is its significance?
For any population with a mean and standard deviation, the distribution of sample means for sample size n will have a mean u and standard deviation SD/square root of n, and will approach a normal distribution as n approaches infinity The theorem describes the distribution of sample means for any population (we can make statistical inferences about any population) and when n=30, the distribution is almost perfectly normal
What is the assumption of homogeneity of variance? How do you test this assumption?
HoV requires that two populations being compared but have equal variances - most important when the discrepancy between sample sizes is large - without satisfying HoV, you cannot interpret a t statistic because you cannot tell which two values is responsible for the outcome HoV can be tested by using the Levene's test in SPSS
What are the advantages of running an experiment with Two Factors between-subjects design compared to running two experiments with One-Factor between-subjects design?
In a one-way ANOVA, it focuses on simply one independent variable and one dependent variable. However, variables rarely exist in isolation in the real world. The two way ANOVA focuses on two independent variables to examine these more complex, real-life situations, thus increasing the external validity of the study. Can measure up to three mean differences at a time
What is the meaning of SS and MS for treatment and error?
MS error only measures the error variability within the treatment conditions (SSwithin)
What is the simple (or multiple) correlation coefficient? What is the squared simple (or multiple) correlation coefficient?
Multiple correlation coefficient (R) - The correlation between one variable (Y) and a set of predictors - Measure of association between a DV and a set of predictors Squared correlation coefficient (R2) - The squared correlation coefficient between Y and a set of one or more predictor variables - The proportion of variance in Y that is predictable from (or accounted for by) a set of predictors
Parametric test vs. nonparametric test: How are they different? (in terms of hypothesis, scale of the data, assumptions).
Parametric Test - t-test and ANOVA - Tests that concern population parameters and require assumptions about parameters - Test hypotheses about population parameters - Requires the three assumptions (normal distribution; homogeneity of variance) - Require numerical score for reach individual - interval or ratio scale Nonparametric Test - Chi-Square - Use sample data to evaluate hypotheses about the proportions or relationships that exist within populations - Do not state hypotheses in terms of parameter and only meet few (if any) assumptions - sometimes called distribution free tests participants usually classified into categories (e.g. Democrat or Republican) involve measurement on the ordinal and nominal scale (frequencies)
What is Type II error?
Researcher fails to reject the null hypothesis when it is actually false. Concludes that there is no treatment effect when there is.
What is the meaning of partial regression coefficient
Specifically, the regression analysis evaluates the contribution of each predictor variable after the influence of the other predictor has been considered. Thus, you can determine whether each predictor variable contributes to the relationship by itself or simply duplicates the contribution already made by another variable. - gives the amount by which the dependent variable (DV) increases when one independent variable (IV) is increased by one unit and all the other independent variables are held constant Changes in DV for one-unit change in each IV, assuming that the other IVs are held constant (i.e. controlling for the effects of the other IVs) Standardized regression coefficients are used to compare the relative contribution of each predictor e.g. b1 is the partial regression coefficient for the regression of Y on X1 "holding X2 constant" b2 is the partial regression coefficient for the regression of Y on X2 "holding X1 constant"
Definition of the standard error of estimate in regression vs. definition of the standard deviation of scores
Standard error of estimate measures the standard distance between the predicted Y values on the regression line and the actual Y values in the data Standard deviation measures the standard distance from the mean Conceptually, standard error of estimate similar to standard deviation because both are a measure of standard error.
What are the sources of variance (SStotal = SSregression + SSresidual)?
The SS regression is the predicted portion of the Y score variability measured by r squared The SS residual is the unpredicted portion of the Y score variability which is found by subtracting the r squared with 1 The SS total is the sum of the SS regression and SS residual
What is the meaning of the effect size?
The effect size used for the regression is R squared. - R squared describes the proportion of the total variability of the Y scores that is accounted for by the regression equation. - r squared measure the percentage of variance accounted for with the single-predictor regression
What is a main effect?
The mean differences among the levels of one factor - the mean differences among the rows describe the main effect of one factor, and the mean differences among the columns describe the main effect for the second factor - matrixes simply DESCRIBE main effects
What is the p-value? What does the p-value become when the null is rejected? (In other words, how is the p-value related to the type I error?)
The p-value is the probability that the observed result would occur if Ho was true (no treatment effect). - also the probability of a Type I error - In case of Type I error, p becomes the new alpha. - In case of Type II error, p becomes the new beta.
What is power?
The probability that the test will correctly reject a false null hypothesis (1-beta) - as the power increases, the probability of a Type II error decreases - increasing sample size increases the power of the test, as well as changing from a two-tailed to a one-tailed test - reducing the alpha level reduces the power of the test
What is alpha?
The probability that the test will lead to a Type I error. - mainly the probability value that is used to define the concept of "very unlikely" in a hypothesis test. - As alpha increases, the chances of committing a Type 1 error decreases
What is beta?
The probability that the test will lead to a the Type II error - The probability of accepting the null hypothesis when its false
What are the differences and similarities between the standard error and the standard deviation?
The standard error provides a measure of how much distance is expected on average between a sample mean and the population mean Standard deviation uses the mean of the distribution as a reference point and measures variability by considering the distance between each score and population mean. Also describes the distribution by telling if individual scores are clustered together or spread apart. The standard error simply serves the same purpose of the standard deviation but for the distribution of sample means 1. describes the distribution of sample means: how much difference is expected from one sample and another 2. measures how well an individual sample mean represents the entire distribution: how much distance is reasonable to expect between a sample mean and the overall mean for the distribution of sample means
When is the unstandardized regression coefficient useful? When is the standardized regression coefficient useful?
The unstandardized regression coefficient is in terms of the original values, or raw-data, scores for X and Y - this equation is easier to compute using raw data The standardized regression coefficient is greatly simplified (X and Y scores converted to z-scores) - useful when the equation needs to be generalized - using the z-score for each X value (zX) to predict the z-score for the corresponding Y value (zY) - the relative size of the beta values is an indication of the relative contribution of the two variables
What are the different kinds of Post Hoc Tests?
Tukey's HSD Test - most commonly used - compute a single value that determines the minimum difference in the scores needed in order to be significant (if mean difference is greater than the HSD value) Scheffe Test - considered the safest - has the smallest risk of a Type I error - uses an F-ratio to evaluate the significance (two mean differences in MS between and the same MS within)
Why use ANOVA instead of multiple t-test? If multiple t-tests are applied, what would be the size of the inflated type I error for a certain (e.g. 3) multiple t-test?
Type I error is a concern - every time you do a hypothesis test, you set an alpha that determines your chance of a type 1 error (e.g. alpha level .05 is a 5% chance of getting a type 1 error). this is known as the test-wise alpha level - the more tests you do, the more risk. this is known as the experiment-wise alpha level, which is the total probability of a type 1 error that is accumulated from all the individual tests in the experiments (e.g. alpha level .05 for three tests adds up to .15 or 15% chance of type 1 error) - ANOVA allows for just one test for all three conditions, and one alpha level to avoid the problem of inflated experiment-wise alpha level
What are the assumptions for both Chi-Square tests?
Violation of assumptions and restrictions casts doubt on results, and increases the probability of a Type 1 error 1. INDEPENDENCE OF OBSERVATIONS: One consequence of independent observations is that each observed frequency is generated by a different individual. A chi-square test would be inappropriate if a person could produce responses that can be classified in more than one category or contribute more than one frequency count to a single category. 2. A chi-square test should not be performed when the expected frequency of any cell is less than 5. The chi-square statistic can be distorted when E is very small by causing a small discrepancy that results in a large value for the chi-square statistic. It is best to have a large sample size.
What is Type I error?
When a researcher rejects the null hypothesis that is actually true. Concludes that there is a treatment effect when there is not.
When and why can you reject the null?
You can reject the null hypothesis when the p-value is less than the set alpha level. If the sample data falls on the critical region
What is the meaning of the size of regression slope (or regression coefficient), for example, what does b = .67 (or β = .23) tell us?
the b is the slope: determines how much the Y variable changes when X is increased beta is the standardized version - beta value is equal to value of the regression coefficients if the predictors and the criterion were in z-score form (i.e. if they were standardized with a mean of zero and a standard deviation of 1). The value is equal to the Pearson correlation of both X and Y.
