Final Exam Conceptual

What are the assumptions associated with applying an ANOVA to data in a factorial design

- Each cell (condition) is associated with it's own population - DV is normally dist. - Homogeneity of pop. variances unequal= 1.5:1 equal = 2.1 - Homogeneity of sample size 1.5:1 - N>7 for each cell

Assume you have a 2 (Age) x 3 (Drug Dose) between groups design. This is a balanced design with 10 scores in each cell and a total of 60 scores in the study. The interaction between Age & Drug Dose reveals a significant Fobs. You (appropriately) apply Tukey's HSD as a probe of this treatment effect. In the formula, what value will you use for n?

10

If null hypothesis is true then the treatment effect will be?

Because the Null Hypothesis is true, it means that the means of the two populations are equivalent, so the treatment effect is 0.

What are the assumptions of the random sampling model & their rational?

Data are scores - stat. test are unique for each type of data/ design Participants are randomly sampled from pop - helps genrate unbiased samples, ensures independence amoung scores DV is normal dist. in pop. - sample, dist will be specific shape - all theoretical crit values are based on the assumption that the DV is normally dist. Homogeneity of pop. variance Each group, condition or cell has at least n>7 scores - hard to reject null when N<7

Choose the BEST multiple comparison test to probe a multi-group analysis given the information provided. Must always do j-1 comparisons. Dunn's Fisher's LSD Tukey's HSD Dunnett's

Dunnett's

A manipulated independent variable must always be either interval or ratio in terms of its measurement scale.

FALSE

Draw a floor effect and ceiling effect

Floor effect- scores are skewed to the mim. scale ceiling effect- scores are skewed to the max scale

Researchers have three primary goals when conducting research. The three goals are listed below. Which goal do only a few researchers truly seek out and is hardest to attain when conducting research? Generalize their findings to the population in order to better understand human behaviour. Control for bias and reduce confounds in their experiments. Examine whether a systematic relationship exists between independent and dependent variables.

Generalize their findings to the population in order to better understand human behaviour.

How do you know if you have met the assumptions for homonegiety of variance?

Levenes output is less than our crit value, then you have met the assumption p>0.05 (p is greater than 0.05)

To check for Homogenity of variance assumption is met you use _____, if it is met then you would use the ___________ test. Then you would conduct a __________ for your a priori predictions. Lastly, if you had a sign f(obs) you would use the _____________.

Levenes test, one way ANOVA. Planned comparisions, post hoc comparisions

In terms of interpreting a multi-factorial design, another term for Multiplicative is

Non-Additive

Why are outliers a probelm?

Outliers will increase our estimated s2, which leads to an increased estimated standard error, which decreases our test ratio making it harder to reject the Null.

define an interaction

The extent to which each level of factor a varied (changed) across each level of factor b.

What are characteristics of the Sampling Distribution for the F-statistic?

The shape is asymmetrical and positively skewed All computed values for the F(statistic) will be positive The measure of central tendency is the median

Under the Random Assignment Model of Hypothesis Testing, if we have a j = 2, c = 2 design, and categorical data, we would use the a. Fisher's Exact Test b. Binomial Exact Test c. Sign Test d. Median Split Test e. 𝜒2 Contingency Table Test f. Factorial ANOVA

a. Fisher's Exact Test

In Step 4 of Hypothesis testing (HT), what is the major change that occurs in multi-factorial designs compared to HT applied to a one-factor design? a.The value for p(obs) must be adjusted based on the number of treatment effects being tested. b.More than one value for Fobs must be computed. Separate values for Fobs must be computed, one for each treatment effect in the study, and one for each interaction. c.This is a trick question; there are no differences. A single value for Fobs is computed for either type of design. d.One value for Fobs is computed as a test of all main effects and a second, separate value for Fobs is computed for all interactions.

b.More than one value for Fobs must be computed. Separate values for Fobs must be computed, one for each treatment effect in the study, and one for each interaction.

What is one of the implications for the scale of measurement of the DV is a. guiding us in choosing the correct graphic figure to display the findings from our study. b. whether our DV is measured or manipulated c. type of statistical analysis applied to the data to test a hypothesis d. whether we randomly assign participants into groups

c. type of statistical analysis applied to the data to test a hypothesis

In Step 4 of Hypothesis testing (HT), what is the major change that occurs compared to HT applied to a one-factor design? a. This is a trick question; there are no differences. A single value for Fobs is computed for either type of design. b.One value for Fobs is computed as a test of all main effects and a second, separate value for Fobs is computed for all interactions. c.More than 1 value for Fobs must be computed. You need separate values for Fobs must be computed, one for each treatment effect in the study. d.The value for p(obs) must be adjusted based on the number of treatment effects being tested.

c.More than 1 value for Fobs must be computed. You need separate values for Fobs must be computed, one for each treatment effect in the study.

Why would you have non-normality in the population?

ceiling/floor effect (+ or - skew in pop). Outliers in data - produces larger values for s^2 and estimated standard wrro and therefore small values for the pobs - large variablity in data

Assume you have a 2 x 4 between groups design. The value for df for each main effect is computed as

j - 1, or the number of levels for that factor - 1.

If there is no random process in your experiment (such as random sampling from the population or random assignment to groups), then you are limited to... establishing cause and effect if the DV is score data and the DV is measured. establishing cause and effect if the DV is score data and the IV is manipulated. establishing an association only between the IV and the DV only using descriptive statistics (no inferences can be made)

only using descriptive statistics (no inferences can be made)

What does "parametric estimation" mean?

population parameters are estimated from sample statistics

Under the Random Assignment Model of Hypothesis Testing for an independent samples design, you conduct Levene's test and you note that p < .05. This means that...

you have nothing to worry about because you do not need to meet the assumption of homogeneity of variance for the Random Assignment Model

what happens when F-test is violated?

- Less robust to violation of assumptions - need homogeneity of variance, and n's within a 1:1.5 ratio

What is the rationale for the homogeneity of variance assumption?

- can pool equal populations into single population - single pooled pop. is used to generate one sample dist. of crit values - pooled variance only need 1 σ2e as an estimate of standard error (se), when j=2, or mean squared error when MSerror for j>2

what happens when t-test is violated?

- t test is moderaley robust to violation - tobs is BIAS value when there is heterogenity of sample n, and heterogeneity of sigma. especially when larger sigma is associated with smaller sample size

What are the characteristics of the t-test and f-test?

- test of parametric estimation - use pop. as refrence point - assumes all assumption of test ratio are met - when sigma and mu are unknown, estimate by using statistics

For an unbalanced ANOVA design (i.e., when there are unequal n within each condition), our assumption of homogeneity of variance states that the ratio of the smaller to the larger variance should be no larger than:

1:1.5

In a related samples design with n = 13, you set p(α) = .052-tailed. Your critical t-value is:[report the exact numerical value from the t-table -- DON'T WORRY ABOUT THE SIGN, it should be ±]

2

One of the assumptions of the Random Sampling Model of Hypothesis testing is that, for an independent samples design, there is homogeneity of population variances, as well as homogeneity of sample sizes. In reality, the F-test is relatively robust to these assumptions as long as the ratio between population variances does not exceed ____ when there are equal n in each cell.

2:1

Assume you have a 2 (Age) x 3 (Drug Dose) between groups design. This is a balanced design with 10 scores in each cell and a total of 60 scores in the study. The main effect of Drug Dose reveals a significant Fobs. You (appropriately) apply Fisher's LSD as a probe of this main effect. Why?

Because you met the assumption for homogeneity of population variance. The significance value for Levene's test was p(obs) > .05 . Because it is the most credible option when you have j = 3.

Strengths and weakness of the factorial ANOVA compared to a 1-way ANOVA

Factorial Combining 2 Factors in one research design, rather than having 2 individual 1-way designs - test for the presence of an INTERACTION ‣ to examine the GENERALIZABILITY of a factor. - compare 2 effects (factors) w/ same participants - reduced unexplained error ( can be more powerful than 1 way)

The assumptions for a factorial design have about the same degree of flexibility as the assumptions for a one-factor design. For example, you can have a ratio of about 4:1 for the largest value to the smallest value for variance in cell means and still meet the assumption for homogeneity of population variances. T or F

False There is very little flexibility for the assumptions in ANOVA, especially when you have an unbalanced design or a design that is very complex (i.e., has multiple factors).

If you convert your score data to an ordinal or a nominal scale of measurement, then you can no longer determine if your data is statistically significant. T or F explain

False You can... you just need to use non-parametric tests.

For both the Random Assignment Model and the Random Sampling Model of Hypothesis Testing, the different conditions within an independent samples design (k = 2) must have equal numbers of participants in each cell (or at least no worse than a 2:1 ratio). T or F

False As long as you at least 3 participants in each cell, the Random Assignment Model does not require homogeneity of sample size.

What is the difference between experiment-wise, family-wise, and per-comparison errorrates

Family-wise/experiment wise Error rate- prob. of making type 1 error for a family of comparisons Error rate- prob of making a type 1 error Error rate per comparison - prob. of making a type 1 error for each individual comparison (set by researcher)

What are the 2 forms of data transformation for fixing the assumption of non-normality in population?

Mathematical applied to scores Moderate + skew - square root transformation Stong + skew = log-linear transformation Extreme + Skew = inverse transformation transform scores to lower scale of measurement (ordinal or tallies) and apply non-parametric test (dist. free test)

What are the fixes for when you violate the assumptions for the Random Sampling Model of HT when data are scores?

No random sampling? - use other random sampling method and randomly assign p's to each condition Voliate homogeneity of Variance? - t-test use SPSS and R recreates the sample dist. to adjust for the inequality of error btw. groups (Welch's test) - F -test: ANOVA nor reliable result use SPSS and R as fix. Sample > 7 (less than) - no fix: use different HT Non-normality of pop. - do data transformations that makes the pop. more kurtotic, maintains ordinal relationship of scores

One of the assumptions of the Random Sampling Model of Hypothesis testing is that, for an independent samples design, there is homogeneity of population variances, as well as homogeneity of sample sizes. In reality, the t-test is relatively robust to these assumptions as long as the ratio between population variances does not exceed [population variance ratio] and the ratio between sample sizes does not exceed [sample size ratio].

Sample size: 2:1 Pop. Variance 4:1

The major difference in Step 1 of Hypothesis Testing between the Random Sampling Model and the Random Assignment Model is

Symbolically, we compare population means for the Random Sampling Model, and sample means for the Random Assignment Model

The Random Sampling Model of Hypothesis testing is based on either theoretical or empirical parameters. T or F

T

Under the Random Assignment Model of Hypothesis Testing, it does not matter if the DV is normally distributed in the Population. t or f

T

The only way to confirm an interaction is to conduct an inferential (statistical) test. T or F

True

If you violate the assumption of homogeneity of variance for random sampling model for the F-test can you use probes?

Yes, you an use the Dunnett's because it adjusts for the violation

In a t-test for an Independent Samples Research Design you are at the greatest risk of making a Type II error when You have violated both assumptions and the larger value for variance is associated with the larger sample size. The assumption of homogeneity of variance is violated. n=15 in one sample and n=35 in the other sample. You have violated both assumptions and the larger value for variance is associated with the smaller sample size.

You have violated both assumptions and the larger value for variance is associated with the larger sample size.

You did not truly randomly sample from population for your study (you used a convenience sample instead). Under the Random Sampling Model, what fixes could you apply?

do not generalize your outcome to the Population make sure there is an alternative form of randomness, such as randomly assigning Participants to groups

Which of the following assumptions unique to the Chi Square Test Expected frequency (E) for each category ≥ 5 the IV must must be nominal or ordinal data the DV must be nominal data nT ≥ 20

each observation is independent of every other observation

The computation for the SS for the interaction between 2 factors can be computed as a subtraction term, that is as: SSr x c = SST - SSe - SSrow - SScol because

it represents all the variability in the data set that has not been accounted for by unexplained error and by the explained variability of the 2 main effects. the structural model represents the partitioning of Total variability in the data set into components of explained and unexplained variability and it is the only other part of explained variability left to compute.

Assume you have a 2 x 4 between groups design. The value for df for the error term is computed as

n-1 (in each cell) summed across all cells. (nT - # of cells)

In Step 4 of Hypothesis Testing, under the Random Sampling Model, we determine the following

observed test value (e.g., tobs or Fobs )

What test ratio's are used in the random sampling model of HT?

t-test and F-tests

If the interaction is not significant, then we can state

the effects of the factor are additive there is independence among factors we can generalize the effects of one factor across the levels of another factor

If we say that the effects of the factors are additive, we can definitely conclude that"

the interaction is not significant

What are the shared assumptions of the Random Sampling Model and the Random Assignment Model of Hypothesis Testing?

there is independence between the scores data are scores

What is the golden rule of showing your data it must be ______ and ______

transparent and objective

One of the issues with the Random Assignment Model is that we need to compute a unique Sampling Distribution for each and every experiment we conduct. This is a problem because

we can't use mathematical theory to define our sampling distribution, and must rely on massive computing power (which is a big problem for complicated designs)

One fix for skewed data is to convert the original data into rank orders. The major problem with this procedure is you cannot determine if differences between your groups are statistically significant you can no longer use a t-test or F-test for inferential testing it is difficult to do without a computer you can unintentionally reverse the order of your data

you can no longer use a t-test or F-test for inferential testing

You have a j = 3 design with 11 Participants in each group, and have found that you your observed F(2, 30) = 6.38. You apply a Fisher's LSD test to probe your analysis using all pairwise comparisons. The value for dfe = 30 and the value for MSe = 8.20. What is the computed critical value, tLSD, you will use to test for significant differences between each pair of group means? Assume that you set your p(α) = .012-tailed.

±3.3578

The symbol for the Standard Deviation of Population 0 in an Independent Samples Research design (j = 2) is

σ0

Distinguish among 3 types of post-hoc probes (Fisher's LSD, Tukey's HSD, Dunnett's) both conceptually and mathematically.

‣ Compute critical value to find the Minimum Mean Difference value needed to reject the null. Fisher's LSD - post hoc: J(j-1)/2 - J=3 - modified t-test to use the MSe value from the ANOVA - Homogeneity can't be violated - normal alpha - Use t-table for crit Tukey's HSD - post hoc : J(j-1)/2 - J>3 - MSe value for ANOVA used for pooled error term - Experiment wise error rate - Homogeneity can't be violated - Use Studentized Q for crit Dunnett's t - Only allowed j-1 (j= # of factors be analysed) - Treatment vs. control - Experiment wise error rate - homogeneity of variance needs to be violated - Dunnett's td table for crit