Assumptions To Evaluate For Statistical Tests

2.

Chi Square Test of Association:

Inclusion of Nonoccurances
Sphericity
Homoscedasticity
Normality
Independence of Observations Between and Within

Correct Answer(s)

A. Inclusion of Nonoccurances
A. Normality
A. Independence of Observations Between and Within

Explanation

The Chi Square Test of Association is used to determine if there is a relationship between two categorical variables. Inclusion of Nonoccurances refers to the fact that the test takes into account both the occurrences and non-occurrences of the variables being studied. Normality means that the data should follow a normal distribution. Independence of Observations Between and Within means that the observations within each category should be independent of each other, as well as the observations between different categories. These three factors are important considerations when conducting a Chi Square Test of Association.

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3.

Matched/Paired Samples T-test:

Normality
Sphericity
Homogeneity of Variance
Independence of Observations Within Groups
Independence Observations Between Groups

Correct Answer(s)

A. Normality
A. Independence of Observations Within Groups

Explanation

The correct answer is Normality and Independence of Observations Within Groups. In a paired samples t-test, the assumption of normality states that the data within each group should be normally distributed. This assumption is important because t-tests are based on the assumption that the sampling distribution of the mean is approximately normally distributed. Additionally, the assumption of independence of observations within groups means that the observations within each group should be independent of each other. This assumption ensures that the observations are not influenced by each other and allows for valid statistical inference.

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4.

Mixed ANOVA:

Homogeneity of Variance
Normality
Homoscedasticity
Independence of Observations Between and Within
Sphericity

Correct Answer(s)

A. Homogeneity of Variance
A. Normality
A. Independence of Observations Between and Within
A. Sphericity

Explanation

The answer includes four assumptions that need to be satisfied for a mixed ANOVA analysis.

1. Homogeneity of Variance: This assumption states that the variances of the dependent variable should be equal across all groups or levels of the independent variables. Violation of this assumption may lead to unreliable results.

2. Normality: This assumption states that the distribution of the dependent variable should be approximately normal within each group or level of the independent variables. Departure from normality may affect the accuracy of the statistical tests.

3. Independence of Observations Between and Within: This assumption states that the observations within each group or level of the independent variables should be independent of each other, and the observations between groups should also be independent. Violation of this assumption may lead to biased results.

4. Sphericity: This assumption applies to repeated measures designs and states that the variances of the differences between all possible pairs of conditions should be equal. Violation of sphericity may affect the validity of the statistical tests.

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5.

Bivariate Correlation:

Linearity
Homoscedasticity
Sphericity
Normality
Independence of Observations Within

Correct Answer(s)

A. Linearity
A. Normality
A. Independence of Observations Within

Explanation

Linearity, Normality, and Independence of Observations Within are all important assumptions for conducting a bivariate correlation analysis. Linearity assumes that there is a linear relationship between the two variables being correlated. Normality assumes that the data is normally distributed. Independence of Observations Within assumes that each observation is independent of the others, meaning that there is no systematic relationship between the observations. These assumptions are necessary for accurate interpretation and inference from the correlation analysis.

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6.

Factorial ANOVA:

Independence of Observations Between and Within
Sphericity
Homogeneity of Variance
Normality
Linearity

Correct Answer(s)

A. Independence of Observations Between and Within
A. Homogeneity of Variance
A. Normality

Explanation

This question is asking about the factors that need to be considered in a factorial ANOVA analysis. The correct answer includes three factors: independence of observations between and within, homogeneity of variance, and normality. These factors are important because they ensure that the assumptions of the ANOVA model are met. Independence of observations ensures that each data point is not influenced by any other data point. Homogeneity of variance assumes that the variance of the dependent variable is equal across all levels of the independent variable. Normality assumes that the dependent variable follows a normal distribution.

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7.

One-way Repeated Measures ANOVA:

Sphericity
Independence of Observations Between
Normality
Independence of Observations Within
Homogeneity of Variance

Correct Answer(s)

A. Sphericity
A. Normality
A. Independence of Observations Within

Explanation

The answer includes three important assumptions for conducting a one-way repeated measures ANOVA. Sphericity assumes that the variances of the differences between all pairs of conditions are equal. Normality assumes that the distribution of the differences between conditions is approximately normally distributed. Independence of observations within assumes that the observations within each condition are independent of each other. These assumptions are necessary for the validity and reliability of the ANOVA results.

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8.

Multiple/Hierarchical Regression:

Homoscedasticity
Linearity
Normality in Arrays
Independence of Observations
Multicollinearity

Correct Answer(s)

A. Homoscedasticity
A. Linearity
A. Normality in Arrays
A. Independence of Observations
A. Multicollinearity

Explanation

Multicollinearity could be considered an "issue" or an assumption.

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9.

Independent Samples T-Test:

Multicollinearity
Independence of Observations Between
Homogeneity of Variance
Independence of Observations Within
Normality

Correct Answer(s)

A. Independence of Observations Between
A. Homogeneity of Variance
A. Independence of Observations Within
A. Normality

Explanation

The correct answer includes Independence of Observations Between, Homogeneity of Variance, Independence of Observations Within, and Normality. These are all assumptions that need to be met in order to perform an independent samples t-test. Independence of Observations Between refers to the assumption that the observations in one group are independent of the observations in the other group. Homogeneity of Variance assumes that the variances of the two groups being compared are equal. Independence of Observations Within assumes that the observations within each group are independent of each other. Normality assumes that the data in each group are normally distributed.

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10.

Bivariate Regression

Independence of Observations
Linearity
Normality in Arrays
Homogeneity of Variance
Homoscedasticity

Correct Answer(s)

A. Independence of Observations
A. Linearity
A. Normality in Arrays
A. Homoscedasticity

Explanation

The correct answer is a list of assumptions that need to be met in order to use bivariate regression analysis. Independence of observations means that the data points are not influenced by each other and are randomly selected. Linearity refers to the relationship between the independent and dependent variables being linear. Normality in arrays means that the data is normally distributed. Homoscedasticity means that the variance of the errors is constant across all levels of the independent variable. These assumptions are important to ensure the validity and reliability of the regression analysis.

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11.

MANOVA:

Normality
Homogeneity of Variance
Linearity
Independence of Observations
Homoscedasticity

Correct Answer(s)

A. Normality
A. Homogeneity of Variance
A. Linearity
A. Independence of Observations
A. Homoscedasticity

Explanation

The answer is a list of assumptions that need to be satisfied in order to use MANOVA (Multivariate Analysis of Variance) effectively. Normality refers to the assumption that the data follows a normal distribution. Homogeneity of Variance means that the variances of the dependent variables are equal across groups. Linearity assumes that the relationship between the dependent and independent variables is linear. Independence of Observations assumes that the observations are independent of each other. Homoscedasticity means that the variances of the residuals are equal across groups. These assumptions are important for the validity and accuracy of the MANOVA results.

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12.

One Sample T-test

Independence of Observations Within
Linearity
Normality
Independence of Observations Between
Homogeneity of Variance

Correct Answer(s)

A. Independence of Observations Within
A. Normality

Explanation

The answer "Independence of Observations Within, Normality" suggests that in order to conduct a one-sample t-test, two assumptions need to be met. Firstly, the observations within the sample should be independent of each other, meaning that the value of one observation does not affect the value of another. Secondly, the data should follow a normal distribution, which means that the majority of the observations should be clustered around the mean with a symmetrical distribution. These two assumptions are important for ensuring the validity and reliability of the results obtained from the one-sample t-test.

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Assumptions To Evaluate For Statistical Tests

One-way Between Groups ANOVA:

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Chi Square Test of Association:

Matched/Paired Samples T-test:

Mixed ANOVA:

Bivariate Correlation:

Factorial ANOVA:

One-way Repeated Measures ANOVA:

Multiple/Hierarchical Regression:

Independent Samples T-Test:

Bivariate Regression

MANOVA:

One Sample T-test