Hypothesis Testing Assumptions
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Questions and Answers

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

discrete

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

<p>parametric</p> Signup and view all the answers

Because the assumptions are very ______, there is little problem of violation of assumptions

<p>general</p> Signup and view all the answers

The process of collecting and compiling sample data may be ______ expensive and ______ time-consuming

<p>less, less</p> Signup and view all the answers

Nonparametric tests, whenever they are applicable, are a great ______

<p>convenience</p> Signup and view all the answers

The arithmetic can be ______ and ______ when samples are large and a computer is not available

<p>tedious, laborious</p> Signup and view all the answers

According to the hypothesis testing, if the p-value is less than or equal to __________, we reject the null hypothesis.

<p>α</p> Signup and view all the answers

The test statistic value calculated in step 3 is __________.

<p>13.0</p> Signup and view all the answers

The Mann-Whitney U test is used for testing hypotheses about __________ populations.

<p>two</p> Signup and view all the answers

One of the assumptions of the Mann-Whitney U test is that the variable observed is a __________ random variable.

<p>continuous</p> Signup and view all the answers

The measurement scale should be at least __________ for the Mann-Whitney U test.

<p>ordinal</p> Signup and view all the answers

The conclusion of the hypothesis testing is that there is no sufficient evidence that the average number of hours is not equal to __________ hours.

<p>1.8</p> Signup and view all the answers

If two or more |D𝑖 | are equal, assign each tied value the ______ of the rank positions occupied by the differences that are tied.

<p>mean</p> Signup and view all the answers

Assign the ______ of |D𝑖 | to its rank.

<p>sign</p> Signup and view all the answers

The test statistic is 1.______ or W- whichever is smaller (denoted by T) for H1: M  Mo.

<p>W+</p> Signup and view all the answers

The tabulated T for n and α/2 can be obtained using the ______ Signed Rank Table of Critical Values.

<p>Wilcoxon</p> Signup and view all the answers

We will use the ______ method of hypothesis testing.

<p>p-value</p> Signup and view all the answers

Reject Ho if ______ − value ≤ α, otherwise do not reject.

<p>p</p> Signup and view all the answers

Test the hypothesis at the ______ level of significance that this particular lamp operates, on the average, 1.8 hours before requiring a recharge.

<p>0.05</p> Signup and view all the answers

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.

<p>Wilcoxon</p> Signup and view all the answers

Error terms are not normally ______________.

<p>distributed</p> Signup and view all the answers

Model fits all but one or few outlier ______________ are present.

<p>observations</p> Signup and view all the answers

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.

<p>linear</p> Signup and view all the answers

Not all variables hypothesized to affect the response variable may have a significant contribution in predicting the mean value of the response ______________.

<p>variable</p> Signup and view all the answers

For any set of k predictors, there will be a total of 2𝑘 possible number of models that can be ______________.

<p>formulated</p> Signup and view all the answers

This calculation is based on the fact that each predictor can be either included or excluded from the ______________.

<p>model</p> Signup and view all the answers

Among the competing models, a final model will be ______________.

<p>adopted</p> Signup and view all the answers

It starts with all predictor variables in the ______________.

<p>model</p> Signup and view all the answers

Correlated independent variables make it difficult to make inferences about the individual ______ coefficients (slopes) and their individual effects on the dependent variable (Y).

<p>regression</p> Signup and view all the answers

An independent variable known to be an important predictor ends up having a ______ regression coefficient that is not significant.

<p>an</p> Signup and view all the answers

A regression coefficient that should have a ______ sign turns out to be negative, or vice versa.

<p>positive</p> Signup and view all the answers

When an independent variable is added or removed, there is a ______ change in the values of the remaining regression coefficients.

<p>drastic</p> Signup and view all the answers

If two independent variables to be included in the model have a statistically significant ______ correlation, they are likely to cause multicollinearity problems.

<p>linear</p> Signup and view all the answers

If condition numbers are between 100 and 1000, there is ______ to strong collinearity.

<p>moderate</p> Signup and view all the answers

A VIF > ______ indicates a multicollinearity problem.

<p>10</p> Signup and view all the answers

One regressor variable is regressed on the remaining regressor variables and the ______ of multiple determination (R2) is computed.

<p>coefficient</p> Signup and view all the answers

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.

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