Experimental Design Test 3

What is the difference between a 2-factor CRD and a 1-way CRD?

Can you add nesting or blocking to a 2-factor CRD?

What are some of the advantages to using a 2-way CRD?

What are some of the drawbacks of using a 2-factor CRD?

What are the assumptions of a 2-factor CRD?

What are the assumptions of a 3-factor CRD?

Each combination of the two factors applied at the same time is a [blank_start]cell[blank_end] containing [blank_start]experimental units[blank_end].

If each cell in a two-factor CRD only contains one experimental unit, the calculations are the same as a [blank_start]Randomized Block ANOVA[blank_end], even though the designs are different.

This is an example of a/an [blank_start]Proportional[blank_end] [blank_start]Balanced[blank_end] design. In this design, [blank_start]n-cells are the same in all cells[blank_end] and tests of cells on diagonal [blank_start]are ok[blank_end].

This is an example of a/an [blank_start]Proportional[blank_end] [blank_start]Unbalanced[blank_end] design. In this design, [blank_start]n-cells are the same in all cells[blank_end] and tests of cells on diagonal [blank_start]are ok[blank_end].

This is an example of a/an [blank_start]Proportional[blank_end] [blank_start]Balanced[blank_end] design. In this design, [blank_start]n-cells are the same in all cells[blank_end] and tests of cells on diagonal [blank_start]are ok[blank_end].

This is the results of an example Two-Factor CRD ANOVA with Multiple Replicates. What kind of interaction is this? [blank_start]No Interaction[blank_end] Can we interpret Main Effects? [blank_start]Yes[blank_end] Would Simple Effects be of interest? [blank_start]Possibly[blank_end]

This is the results of an example Two-Factor CRD ANOVA with Multiple Replicates. What kind of interaction is this? [blank_start]No Interaction[blank_end] Can we interpret Main Effects? [blank_start]Yes[blank_end] Would Simple Effects be of interest? [blank_start]Possibly[blank_end]

This is the results of an example Two-Factor CRD ANOVA with Multiple Replicates. What kind of interaction is this? [blank_start]No Interaction[blank_end] Can we interpret Main Effects? [blank_start]Yes[blank_end] Would Simple Effects be of interest? [blank_start]Possibly[blank_end]

This is the results of an example Two-Factor CRD ANOVA with Multiple Replicates. What kind of interaction is this? [blank_start]No Interaction[blank_end] Can we interpret Main Effects? [blank_start]Yes[blank_end] Would Simple Effects be of interest? [blank_start]Possibly[blank_end]

Label the interaction graphs

Simple effects or cell means testing is usually done with the interaction effect in the Two-Factor ANOVA is _______, and interpreting main effects of column and row means does not make sense.

Sevearal different approaches can be used to examine simple effects. The primary differences in the approaches deal with control of ____________ and ____________ considerations

What "logical" sets of simple effects exist?

In a Two-Factor ANOVA, if interaction is large and it has been decided that the main effects cannoth be interpreted, can we ignore the two-factor design and analyze each column/row with separate One-Factor Completely Randomized ANOVAs?

Is ignoring the two-factor design and running separate One-Factor ANOVAs or t-tests more or less powerfal than constructing the simple effects tests ithin the context of the Towo-Factor ANOVA? Why?

Model I: [blank_start]fixed - 2 fixed factors[blank_end] Model II: random - [blank_start]2 random factors[blank_end] Model III: mixed - [blank_start]1 fixed factor, 1 random factor[blank_end]

Testing for interaction is...

What are the null hypotheses of a Two-Factor Completely Randomized ANOVA with Multiple Replicates? (hint: main effects)

What are the assumptions of a Two-Way Completely Randomized ANOVA (Model I) with Multiple Replicates?

What steps should be taken after the main Two-Way ANOVA?

Select all that apply to Type I SS

Select all that apply to Type II SS

Select all that apply to Type III SS

With balanced data, all SS methods (Type I, II, III) will yield the same results.

SS will be the same for two entries in all computation methods (Type I, II, III). Which two?

In the presence of significant interaction, the chosen method of SS is _________.

Which of these are ways to DIRECTLY interpret interaction in a Two-Factor ANOVA?

Main effects for Factor A by this method can be interpreted as the main effect of Factor a controling or adjusting for Factor B and the interaction of Factor A x Factor B.

A major criticisim of this method is that the model does not respect marginality, and that it is generally wrong to interpretmain effects in the presence of an interaction.

In this method, SS for main effects are computed adjusting fo other main effects in the model, but omitting interaction terms.

In this method of SS computation, effects are adjusted only for the terms that appear "above" them in the ANOVA table.

A criticism of this SS computation method is that it produces different values for SS if we swap the ordering of the factors.

The null hypothesses associated with this method can be interpreted as the equcivalenc eof unweighted means without making further assumptions regarding the presence of interaction.

This method simplifies the testing of equality of equally weighted means if the interaction term is assumed to be zero.

If we can assume there's no interaction, the hypotheses for the Type I method become equivalent to Type III

This method tests for equivalence of fully weighted means for the first variable entered into the model, and the null hypothesis for the second factor is the same as the Type II method.

A criticisim for these methods of SS computation is that the null hypotheses are a function of sample size.

If ther is no interaction, this SS computation mehtod is the most powerful for an unbalanced design.

For most situations, power of the method of SS computation depends primarily on what?

Procedure for Aligned Rank Transform for a Two-Factor ANOVA 1. [blank_start]Align[blank_end] data [blank_start]seperately[blank_end] producing [blank_start]three[blank_end] different data sets 2. [blank_start]Rank aligned[blank_end] data [blank_start]all together[blank_end] [blank_start]within[blank_end] each of the [blank_start]three[blank_end] data sets 3. Replace original data with [blank_start]ranks[blank_end] [blank_start]within[blank_end] each of the [blank_start]three[blank_end] data sets 4. Run [blank_start]three[blank_end] [blank_start]separate[blank_end] [blank_start]Two-Factor[blank_end] ANOVAs on [blank_start]ranks[blank_end]

A _______ is another version of a two-factor experiment, with one factor nesed within the second factor.

Match the design types with the correct image.

Procedure for Aligned Rank Transform for a Three-Factor ANOVA 1. [blank_start]Align[blank_end] data [blank_start]seperately[blank_end] producing [blank_start]three[blank_end] different data sets 2. [blank_start]Rank aligned[blank_end] data [blank_start]all together[blank_end] [blank_start]within[blank_end] each of the [blank_start]three[blank_end] data sets 3. Replace original data with [blank_start]ranks[blank_end] [blank_start]within[blank_end] each of the [blank_start]three[blank_end] data sets 4. Run [blank_start]three[blank_end] [blank_start]separate[blank_end] [blank_start]Two-Factor[blank_end] ANOVAs on [blank_start]ranks[blank_end]

_____________ is a common technique for estimating coefficients of linear regression equations.

Linear regrassion equations describe the relationship beetween one or more [blank_start]independent[blank_end] [blank_start]quantitative[blank_end] variables and a [blank_start]dependent[blank_end] variable.

What are the purposes of OLS? (One-Factor ANOVA with x as independent variable and y as dependent variable)

In which situations can OLS be used?

OLS assumes error in...

Which line is the middle line of the data (Error in both the x and y direction)?

The OLS method aims to minimize the [blank_start]sum of squre differences[blank_end] between the observed and predicted values.

The main question that OLS aims to answer is whether or not there is a treatment effect (presence or absence of change).

[blank_start]Prediction Intervals[blank_end]: related to individual points in a dataset that was predicted mathematically. [blank_start]Prediction Bands[blank_end]: related to the entire OLS line from the new dataset that was predicted mathematically [blank_start]Confidence Intervals[blank_end]: related to individual points in the actual dataset [blank_start]Confidence Bands[blank_end]: related to the entire OLS line from the new dataset that was predicted mathematically

Steps of inverse prediction: 1. Measure the [blank_start]dependent[blank_end] variable ([blank_start]y[blank_end]) at known values of the [blank_start]independent[blank_end] variable ([blank_start]x[blank_end]). 2. Use these values to create a [blank_start]standard curve[blank_end] and find the regression equation 3. Rearrange the regression, isolating [blank_start]x[blank_end] on one side 4. Measure the unknown, finding the [blank_start]y-value[blank_end] 5. Plug the measurement into the rearranged equation to find the unknown value

[blank_start]Interpolation[blank_end]: using the section of the OLS line bounded by the dataset for data prediction ([blank_start]good use of equation[blank_end]) [blank_start]Extrapolation[blank_end]: using sections of the OLS line not bounded by the dataset in order to complete data prediction ([blank_start]not recommended[blank_end])

Common Diagnostic Tests for OLS [blank_start]Scatter Plot of Y vs X[blank_end] -initial visual diagnostic -may indicate [blank_start]non-linear patterns[blank_end] r^2 -some information on the [blank_start]linear relationship between X and Y[blank_end] -as a general rule, r^2 > [blank_start]0.95[blank_end] indicates a strong linear relationship [blank_start]Durbin-Watson Test[blank_end] -indication of [blank_start]autocorrelation[blank_end] or non-random error terms -ranges from 0-4 - 2=[blank_start]low autocorrelation[blank_end], near 1 or 4 = [blank_start]high autocorrelation[blank_end] [blank_start]Diagonal Elements of the hat matrix[blank_end] -indication of X outlier [blank_start]Studentized Residual[blank_end] -examines patterns on scatter plot of Studentized Residual vs. X -any pattern other than random indicates potential issues with [blank_start]linearity or HOV[blank_end] [blank_start]Studentized Deletion REsidual[blank_end] -large [blank_start]absolue alues[blank_end] indicate possible Y-outliers -absolute SDR value in 2-3 range or greater indicate possible outlier [blank_start]Cook's Distance[blank_end] -large values indicate [blank_start]influential Y data point[blank_end] on linear equation -percentiles greater than [blank_start]50[blank_end]% indicate overly influential data point. [blank_start]95[blank_end]% would be extreme.

r^2 = [blank_start]1[blank_end] indicates a perfect line r=[blank_start]1[blank_end] indicates perfect positive correlation r=[blank_start]-1[blank_end] indicates perfect negative correlation r=[blank_start]0[blank_end] indicates no correlation

Transformation of X --corrects non-linearity without changing [blank_start]variance[blank_end] and [blank_start]distribution of Y-values[blank_end] Transformation of Y --corrects non-linearity of [blank_start]relation between X and Y[blank_end] --correct [blank_start]HOV[blank_end] and [blank_start]non-normal distribution of Y values[blank_end] Transformation of both X and Y --correct non-linearity [blank_start]imposed by transformations[blank_end] to fix other issues

[blank_start]Autoregressing Models[blank_end] --regression taking [blank_start]autocorelation[blank_end] into account --usually based on measuring things over time [blank_start]Logistic Regression[blank_end] --Regression of discrete categorical data ([blank_start]age, presence/absence[blank_end]) [blank_start]Curvilinear Regression[blank_end] --fitting polynomial curves ([blank_start]cubic, quadratic, etc.[blank_end] [blank_start]Nonlinear Regression[blank_end] --fitting [blank_start]S-shaped curves[blank_end] --commonly used for growth curves [blank_start]Spline Regression[blank_end] --using [blank_start]splines and knots[blank_end] to fit separate sections of complex patterns --good for fit, not great for prediction [blank_start]Multiple Regression[blank_end] --similar to linear regression in many aspects, but more than one X variable --uses [blank_start]dummy X matrix[blank_end]

ANCOVA is a full design.

In ANCOVA, for each individual [blank_start]EU/MU[blank_end] [blank_start]a covariate[blank_end] is measured to account for variation other than the treatment effect.

ANCOVA can be applied to any design, including designs that also have blocking

ANCOVA is primarily utilized for what purpose?

What is the null hypothesis of ANCOVA?

What is the null hypothesis of Goodness of Fit?

What is the null hypothesis of linear correlation?

What are the assumptions for Y (data) for using a covariate in a One-Factor CRD?

What are the assumptions for X (covariate) for using a covariate in a One-Factor CRD?

What are the assumptions for X and Y for using a covariate in a One-Factor CRD?

What is the main purpose for linear correlation?

What are the assumptions of Pearson's Correlation?

What are the assumptions of Spearman Non-Parametric Correlation?

[blank_start]r[blank_end] = Pearson correlation coefficient [blank_start]r^2[blank_end] = coefficient of determination

[blank_start]OLS[blank_end] lines are used for prediction [blank_start]Central Axis[blank_end] lines are used for function

In a t-test of the correlation coefficient, the null hypothesis is [blank_start]r = rho = 0[blank_end]. For a two-tailed test, t follows the [blank_start]t[blank_end]-distribution with v degrees of freedom.

z and z* transforms and the z-test of the correlation coefficient is used for testing which null hypotheses?

Which is one of the best non-parametric procedures for testing correlation?

The Spearman Non-Parametric procedures of determining correlation is often used by default because it doesn't rely on normality or linearity, but still gives reliable conclusions.

Analysis of Frequency/Count data relies on the testing of ___________ and ____________.

What count-data design(s) can be analyzed with Goodness of Fit?

What count-data design(s) can be analyzed with Contingency Tables?

What is the null hypothesis for Goodness of Fit?

What is the null hypothesis for Contingency Tables?

What is the null hypothesis for Homogeneity Log-likelihood tests??

What are the assumptions for Goodness of Fit?

What are the assumptions for Contingency Tables?

Chi-squared test uses [blank_start]x^2[blank_end] statistic, which follows the [blank_start]x^2[blank_end] distribution table with v degrees of freedom. Log-likelihood test uses the [blank_start]G[blank_end] statistic, which follows the [blank_start]x^2[blank_end] distribution table with v degrees of freedom.

Heterogeneitiy Log-Likelihood Tests analyze [blank_start]correlation[blank_end] by combining [blank_start]Goodness of Fit[blank_end] tests.

If the heterogeneity G test does not reject the null hypothesis of homogeneity across all tests, the [blank_start]Pooled G[blank_end] test is a legitimate test of adding the counts of all tests together for a combined test with a larger number of counts.

The purpose of this test is to add counts of multiple Godness-of-fit tests for a combined test with a larger number of counts.

The purpose of this test is to test for homogeneity of goodness-of-fit tests (log-likelihood), particularly before a Pooled G test.

Contingency tables can have marginal totals that are either fixed or not fixed. [blank_start]Both fixed[blank_end] ([blank_start]very rare[blank_end]) Control totals of both factors, but not counts of each cell In other words: control ratio between rows/columns, but not ratios of counts within each row/column [blank_start]Both margins not fixed[blank_end] (common) Don't control totals of each row/column, only the total N In other words: don't control any ratios [blank_start]One margin fixed, one margin not[blank_end] ([blank_start]common[blank_end]) Control totals of one facor (rows OR columns), but not the other. In other words: control the ratio of either rows OR columns, but not the other.