Podcast
Questions and Answers
Nonparametric procedures may be applied when the data are measured on a ______ measurement scale
Nonparametric procedures may be applied when the data are measured on a ______ measurement scale
weak
The test statistic in most cases is a ______ random variable
The test statistic in most cases is a ______ random variable
discrete
Nonparametric procedures have a reputation for requiring only ______ calculations when samples are large
Nonparametric procedures have a reputation for requiring only ______ calculations when samples are large
simple
The careful research worker always asks himself first whether he can use a ______ test
The careful research worker always asks himself first whether he can use a ______ test
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Because the assumptions are very ______, there is little problem of violation of assumptions
Because the assumptions are very ______, there is little problem of violation of assumptions
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The process of collecting and compiling sample data may be ______ expensive and ______ time-consuming
The process of collecting and compiling sample data may be ______ expensive and ______ time-consuming
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Nonparametric tests, whenever they are applicable, are a great ______
Nonparametric tests, whenever they are applicable, are a great ______
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The arithmetic can be ______ and ______ when samples are large and a computer is not available
The arithmetic can be ______ and ______ when samples are large and a computer is not available
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According to the hypothesis testing, if the p-value is less than or equal to __________, we reject the null hypothesis.
According to the hypothesis testing, if the p-value is less than or equal to __________, we reject the null hypothesis.
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The test statistic value calculated in step 3 is __________.
The test statistic value calculated in step 3 is __________.
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The Mann-Whitney U test is used for testing hypotheses about __________ populations.
The Mann-Whitney U test is used for testing hypotheses about __________ populations.
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One of the assumptions of the Mann-Whitney U test is that the variable observed is a __________ random variable.
One of the assumptions of the Mann-Whitney U test is that the variable observed is a __________ random variable.
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The measurement scale should be at least __________ for the Mann-Whitney U test.
The measurement scale should be at least __________ for the Mann-Whitney U test.
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The conclusion of the hypothesis testing is that there is no sufficient evidence that the average number of hours is not equal to __________ hours.
The conclusion of the hypothesis testing is that there is no sufficient evidence that the average number of hours is not equal to __________ hours.
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If two or more |D𝑖 | are equal, assign each tied value the ______ of the rank positions occupied by the differences that are tied.
If two or more |D𝑖 | are equal, assign each tied value the ______ of the rank positions occupied by the differences that are tied.
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Assign the ______ of |D𝑖 | to its rank.
Assign the ______ of |D𝑖 | to its rank.
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The test statistic is 1.______ or W- whichever is smaller (denoted by T) for H1: M Mo.
The test statistic is 1.______ or W- whichever is smaller (denoted by T) for H1: M Mo.
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The tabulated T for n and α/2 can be obtained using the ______ Signed Rank Table of Critical Values.
The tabulated T for n and α/2 can be obtained using the ______ Signed Rank Table of Critical Values.
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We will use the ______ method of hypothesis testing.
We will use the ______ method of hypothesis testing.
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Reject Ho if ______ − value ≤ α, otherwise do not reject.
Reject Ho if ______ − value ≤ α, otherwise do not reject.
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Test the hypothesis at the ______ level of significance that this particular lamp operates, on the average, 1.8 hours before requiring a recharge.
Test the hypothesis at the ______ level of significance that this particular lamp operates, on the average, 1.8 hours before requiring a recharge.
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For the sake of an illustration, we will just use the ______ Signed Ranks test without testing the normality of the data or whether we met the assumptions of using t-test.
For the sake of an illustration, we will just use the ______ Signed Ranks test without testing the normality of the data or whether we met the assumptions of using t-test.
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Error terms are not normally ______________.
Error terms are not normally ______________.
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Model fits all but one or few outlier ______________ are present.
Model fits all but one or few outlier ______________ are present.
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Our objective in this subsection is to come up with a model that describes the relationship of the predictor variables with a continuous dependent variable in a ______________ fashion.
Our objective in this subsection is to come up with a model that describes the relationship of the predictor variables with a continuous dependent variable in a ______________ fashion.
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Not all variables hypothesized to affect the response variable may have a significant contribution in predicting the mean value of the response ______________.
Not all variables hypothesized to affect the response variable may have a significant contribution in predicting the mean value of the response ______________.
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For any set of k predictors, there will be a total of 2𝑘 possible number of models that can be ______________.
For any set of k predictors, there will be a total of 2𝑘 possible number of models that can be ______________.
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This calculation is based on the fact that each predictor can be either included or excluded from the ______________.
This calculation is based on the fact that each predictor can be either included or excluded from the ______________.
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Among the competing models, a final model will be ______________.
Among the competing models, a final model will be ______________.
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It starts with all predictor variables in the ______________.
It starts with all predictor variables in the ______________.
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Correlated independent variables make it difficult to make inferences about the individual ______ coefficients (slopes) and their individual effects on the dependent variable (Y).
Correlated independent variables make it difficult to make inferences about the individual ______ coefficients (slopes) and their individual effects on the dependent variable (Y).
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An independent variable known to be an important predictor ends up having a ______ regression coefficient that is not significant.
An independent variable known to be an important predictor ends up having a ______ regression coefficient that is not significant.
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A regression coefficient that should have a ______ sign turns out to be negative, or vice versa.
A regression coefficient that should have a ______ sign turns out to be negative, or vice versa.
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When an independent variable is added or removed, there is a ______ change in the values of the remaining regression coefficients.
When an independent variable is added or removed, there is a ______ change in the values of the remaining regression coefficients.
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If two independent variables to be included in the model have a statistically significant ______ correlation, they are likely to cause multicollinearity problems.
If two independent variables to be included in the model have a statistically significant ______ correlation, they are likely to cause multicollinearity problems.
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If condition numbers are between 100 and 1000, there is ______ to strong collinearity.
If condition numbers are between 100 and 1000, there is ______ to strong collinearity.
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A VIF > ______ indicates a multicollinearity problem.
A VIF > ______ indicates a multicollinearity problem.
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One regressor variable is regressed on the remaining regressor variables and the ______ of multiple determination (R2) is computed.
One regressor variable is regressed on the remaining regressor variables and the ______ of multiple determination (R2) is computed.
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Study Notes
Nonparametric Procedures
- Nonparametric procedures have little problem of violating assumptions and less opportunity for inappropriate and indiscriminate application.
- They can be applied when the data are measured on a weak measurement scale, such as count data or rank data.
- The test statistic in most cases is a discrete random variable with nonzero probabilities assigned to only a finite number of values.
Advantages of Nonparametric Procedures
- The process of collecting and compiling sample data may be less expensive and less time-consuming.
Disadvantages of Nonparametric Procedures
- The calculations needed for most nonparametric procedures are simple and rapid, which may lead to the misuse of parametric procedures.
- The arithmetic can be tedious and laborious, even with large samples and no computer available.
Wilcoxon Signed Ranks Test
- The test statistic is the smaller of W+ or W-.
- Decision Rule: Reject Ho if p-value ≤ α, otherwise do not reject.
- The p-value method of hypothesis testing is used.
Mann-Whitney U Test
- Assumptions:
- The data consists of a random sample of observations from two populations with unknown medians.
- The two samples are independent.
- The measurement scale is at least ordinal.
- The variable observed is a continuous random variable.
- The distribution functions of the two populations differ only with respect to location, if they differ at all.
Model Building
- Objective: to come up with a model that describes the relationship of the predictor variables with a continuous dependent variable in a linear fashion.
- Model selection procedures are needed to choose the “best” set of regressor variables.
Common Variable Selection Procedures
- Backward Selection Procedure: starts with all predictor variables in the model.
- Forward Selection Procedure: starts with no predictor variables in the model.
Multicollinearity
- Clues indicating problems with multicollinearity:
- An independent variable known to be an important predictor ends up having a non-significant regression coefficient.
- A regression coefficient that should have a positive sign turns out to be negative, or vice versa.
- When an independent variable is added or removed, there is a drastic change in the values of the remaining regression coefficients.
- Formal methods to detect multicollinearity:
- Correlation matrix of independent variables
- Condition index or condition number
- Variance Inflator Factor (VIF)
- Tolerance value
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Description
This quiz covers the assumptions of hypothesis testing, including the properties of the test statistic and the general assumptions of hypothesis testing procedures.
