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BioStat > Exam 3 - December 9th > Flashcards

Exam 3 - December 9th Flashcards

1
Q

What sort of test would you use on a data set with a quantitative response variable and no explanatory variable?

A

One-Sample T

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2
Q

What sort of tests could potentially be used on data sets with a quantitative response variable and one categorical explanatory variable?

A

Two-Sample T, Paired T, One-Way ANOVA

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3
Q

What sort of tests could potentially be used on data sets with a quantitative response variable variable, one categorical explanatory variable, and two groups?

A

Two-Sample T or Paired T

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4
Q

What sort of test would you use on a data set with a quantitative response variable, one categorical explanatory variable, and two independent groups?

A

Two-Sample T

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5
Q

What sort of test would you use on a data set with a quantitative response variable, one categorical explanatory variable, and two dependent groups?

A

Paired T

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6
Q

What sort of test would you use on a data set with a quantitative response variable, one categorical explanatory variable, and more than two groups?

A

One-Way ANOVA

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7
Q

What sort of test would you use on a data set with a quantitative response variable and two categorical explanatory variables?

A

Two-Way ANOVA

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8
Q

What sort of test would you use on a data set with a quantitative response variable and one quantitative explanatory variable?

A

Simple Linear Regression

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9
Q

What sort of test would you use on a data set with a categorical response variable and no explanatory variable?

A

One-Sample Proportion

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10
Q

What sort of test would you use on a data set with a categorical response variable and one explanatory variable?

A

Two-Sample Proportion

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11
Q

What is the factor effects model for the two-way ANOVA?

A

Yijk = μ + 𝞪I + 𝜷J + (𝞪𝜷)IJ + εijk

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12
Q

What does the factor effects model for the two-way ANOVA mean?

A

Each observation is equal to the overall mean, plus the effects of Factor A, Factor B, and the interaction between them, plus some error

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13
Q

What are the constraints for the Two-Way ANOVA?

A

∑ 𝞪I = ∑ 𝜷J = ∑ 𝞪𝜷IJ = 0

Zero-Sum Constraint

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14
Q

How can you check the constraint for the Two-Way ANOVA?

A

For Main Effects: The sum the means for each level of factor A (or B) minus the overall mean is zero
- if a and b = 2, half of the individuals are at each level (A1, A2, B1, and B2)

For Interaction: The sum of the means at each treatment combination, minus the means for factor level A, minus the means for factor level B, plus the overall mean is zero
- if a and b = 2, one-quarter of the individuals are in each treatment combination

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15
Q

What are the assumptions for the Two-Way ANOVA?

A

Optional → Equal Sample Sizes or Balanced Design, same number of individuals at each treatment combination

εijk (IID) ~ N(0, σ^2) → Errors are normal, independent, and have constant variance

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16
Q

What is an interaction plot for a Two-Way ANOVA?

A

Plot means for each treatment combination against
levels of a factor, with different lines for each factor

Parallel lines indicate no interaction, crossing lines indicate a possible interaction

Can be antagonistic or reinforcing/synergistic

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17
Q

If there is a significant interaction for a Two-Way ANOVA, how does that change the interpretation of the main effects?

A

You cannot interpret the main effects separately, and must instead conduct a Tukey Pairwise Comparison to test for Factor A effects for each level of Factor B and vice versa

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18
Q

What is the Two-Way ANOVA hypothesis for the main effects?

A

Main Effect A → H0: 𝞪I = 0 for all I versus HA: Not all 𝞪I equal zero

Main Effect B → H0: 𝜷J = 0 for all J versus HA: Not all 𝜷J equal zero

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19
Q

What is the Two-Way ANOVA hypothesis for interaction?

A

Interaction → H0: (𝞪𝜷)IJ = 0 for all I, J versus HA: Not all (𝞪𝜷)IJ equal zero

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20
Q

What is the next step for the Two-Way ANOVA if the interaction is found to be significant?

A

Both factors are important and main effects need to be analyzed using pairwise comparisons (instead of F tests)

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21
Q

What is the next step for the Two-Way ANOVA if the interaction is not significant, but a two level main effect is?

A

State level with higher mean

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22
Q

What is the next step for the Two-Way ANOVA if the interaction is not significant, but a multilevel main effect is?

A

Use Tukey Pairwise Comparisons to test for levels that are significantly different, state higher mean

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23
Q

How can you check the assumptions for a Two-Way ANOVA?

A

Normal Probability Plot of Residuals
Residuals versus Fitted/Factor Levels
Residuals versus Order/Time

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24
Q

Define sample size, effect size, significance level, and power

A 
Sample size (n) - number of subjects in the study
Effect size (△/σ) - effect relative to noise
Significance level (𝞪) - probability of false positive
Power (1-𝜷) - probability of true positive
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25
Q

Using a power-curve for a One-Way ANOVA, how can you determine the sample sizes for a Two-Way ANOVA?

A

Sample size of graph is per group (particular treatment combination), choose alpha and power and use σ = √MSE from a previous study

26
Q

What is the model for the additive Two-Way ANOVA?

A

Yijk= μ + 𝞪I + 𝜷J + + εijk

27
Q

What are the constraints for the additive Two-Way ANOVA?

A

Used when there is only one replicate per treatment combination

Zero-Sum Constraint

28
Q

What are the assumptions for the additive Two-Way ANOVA? How can you check the ones that are different from a regular Two-Way ANOVA?

A

εijk (IID) ~ N(0, σ^2) → Errors are normal, independent, and have constant variance

Interaction terms are assumed to be zero (Interaction Plot)

29
Q

Why does the additional assumption for additive Two-Way ANOVAs exist?

A

With only one replicate per treatment, there are not enough degrees of freedom for both interaction and error

30
Q

What is a Randomized Complete Block Design? (RCBD)

A

A specialized form of the additive Two-Way ANOVA used when experimental units are non-homogeneous

Blocks and treatments are assumed not to interact

31
Q

What is a “block” in a Randomized Complete Block Design?

A

One block is a complete replication of the set of treatments

In agricultural studies, a block is one field and different sections of the field have different treatments

32
Q

What is the model for a Randomized Complete Block Design (RCBD)?

A

Yijk = μ + 🇹I + 𝜷J + + εijk

33
Q

How is a multifactor ANOVA different from a Two-Way ANOVA in terms of analysis?

A

If the three-way interaction or multiple two-way interactions are significant, analyze the three factors jointly (in terms of treatment ABC)

If only one two-way interaction is significant, analyze that interaction and the remaining main effect

If no interactions are significant, analyze main effects separately

34
Q

What is the model for a simple linear regression?

A

YI = 𝜷0 + 𝜷1*XI + εI

35
Q

What are the assumptions for a simple linear regression?

A

εijk (IID) ~ N(0, σ^2) → Errors are normal, independent, and have constant variance

There is a linear relationship

36
Q

How do you check the general assumptions for a simple linear regression?

A

Check with residuals
Sequence Plot
Normal Probability Plot or Histogram
Residuals vs X or Y

37
Q

How do you check the main assumption of a simple linear regression?

A

Scatterplot of values
explanatory variable on the x-axis and the response on the y-axis

Residuals vs X or Y

38
Q

What are the “fitted values” and “residuals” for a simple linear regression?

A

residuals are the distances between observed and predicted values

Predicted/Fitted Values → Points on the regression line above or below observed

39
Q

What is the meaning of the “scope” of a simple linear regression?

A

Scope - Range of data points
Predictions within range are valid, termed interpolation
Predictions outside of range are termed extrapolation

40
Q

What is the significance of the correlation coefficient r for the simple linear regression?

A

Describes the strength and direction of the linear relationship between the variables
greater than .8 is strong, less than .5 is weak

41
Q

What is the significance of the coefficient of determination R^2 of a simple linear regression?

A

R2 is the coefficient of determination or the proportion of Y’s variance that is explained by the regression of Y on X

42
Q

Describe “least squares estimation” in terms of the simple linear regression

A

Slope and intercept are chosen to minimize the sum of the squared residuals

43
Q

What is the equation for a fitted regression line of a simple linear regression?

A

Fitted Line is YI-hat = 𝜷0-hat + 𝜷1-hat*XI

44
Q

Generally, what can a simple linear regression say about the variables that produce its data set?

A

determines the presence of a linear correlation, Causation can only be identified by randomization trials

45
Q

What data transformations (2) could be used to fix the broken assumption of a linear relationship in a simple linear regression?

A

Y = 𝜷0 + 𝜷1X + 𝜷2X2 for a Quadratic Relationship

Transformation of Explanatory Variable X (LnX, √X, X#, 1/X#)

46
Q

What data transformations (2) could be used to fix the broken assumption of constant variance in a simple linear regression?

A

Transformation of Response Variable Y (Box-Cox, 1=no transformation, 0=Ln)
Weighted Least-Squares

47
Q

How do you analyze Box-Cox output?

A

number is data point^#, 1 is no transformation and 0 is natural log

48
Q

What data transformations (2) could be used to fix the broken assumption of normal errors in a simple linear regression?

A

Transformation of Y

Different Response Types (Binomial - Categorical, Poisson - Count)

49
Q

What data transformation could be used to fix the broken assumption of a lack of major outliers in a simple linear regression?

A

Robust Regression Analysis can reduce the impact of outliers

50
Q

What are the hypothesis tests and test statistic for a significant linear relationship for a simple linear regression?

A

H0: 𝜷1 = 0 versus HA: 𝜷1 ≠ 0
T-Statistic: 𝜷1 / SE(𝜷1)
Follows a t-distribution with n-2 degrees of freedom

51
Q

What is the equivalence of the F and t tests for a simple linear regression?

A

The square of the t-statistic (𝜷1 / SE(𝜷1)) is exactly the same as the f-statistic (MS regression / MS error) for a simple linear regression when the numerator degrees of freedom for the F-test is 1

52
Q

What is the difference between a confidence interval for mean response and a prediction interval for a simple linear regression?

A

Prediction Intervals will always be wider than Confidence Intervals of mean response because they take into account error and deviation from the mean

53
Q

When is it appropriate to conduct tests and confidence intervals for the intercept of a simple linear regression?

A

When the intercept (X=0) is practically significant and within the scope of the data

54
Q

When would you conduct a one-sample proportion?

A

Categorical Response (Proportion), No Explanatory Variable

Estimate true proportion/frequency of one of two possible categorical responses and compare to proposed proportion/frequency

55
Q

What is the hypothesis test for a one-sample proportion?

A

H0: p = p0 or HA: p (>,

56
Q

How do you go from the test statistic for a one-sample proportion to the p-value using the standard normal table?

A

Find number corresponding to z score (narrow by nearest .1 on left column and narrow by nearest .01 by top row)

Area/Proportion below Z = table value
Area/Proportion above Z = 1 - table value

57
Q

When would you conduct a two-sample proportion?

A

Categorical Response (Proportion), One Explanatory Variable

Compare true proportion/frequency of one of two possible categorical responses between two groups

58
Q

When would you conduct a Chi-Square test for Association?

A

checking for an an association between one categorical variable and another using a frequency table of the number of observations in each combination of categories

59
Q

When would you conduct a Chi-Square test for Goodness of Fit?

A

checking for how well experimental data fit a certain theoretical distribution

60
Q

What is the difference between a Chi-Square test for Association and Goodness of Fit?

A

The expected counts come from a theoretical distribution, not from a lack of association

BioStat (3 decks)

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