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Measurement Scale Types, Test Stats & Probability

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A: Which of these measurement scales (nominal, ordinal, interval and ratio) can be handled through hypothesis testing?

B: What are the five steps in hypothesis testing? Is the order important? Why or why not?

C: Just what do we mean by "test statistic"?

D: Why do null and alternative hypotheses have to be mutually exclusive?

E: A z-score table shows probability values for a portion of the normal. How would you arrive at a probability value (given in the z-score table) to reflect a two-tailed hypothesis? How would you arrive at a probability value to reflect a one-tailed hypothesis?

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The solution examines measurement scale types, test statistic and probability.

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Measurement scale types, test stats, probability
Please provide detailed explanations for the following:

A: Which of these measurement scales (nominal, ordinal, interval and ratio) can be handled through hypothesis testing?

B: What are the five steps in hypothesis testing? Is the order important? Why or why not?

C: Just what do we mean by "test statistic"?

D: Why do null and alternative hypotheses have to be mutually exclusive?

E: A z-score table shows probability values for a portion of the normal. How would you arrive at a probability value (given in the z-score table) to reflect a two-tailed hypothesis? How would you arrive at a probability value to reflect a one-tailed hypothesis?

Solution:
A: Which of these measurement scales (nominal, ordinal, interval and ratio) can be handled through hypothesis testing?

Data Analysis & Interpretation Descriptive statistics Note: Every criterion applies also to lower levels, eg. "mode" applies to ordinal, interval and ratio data as well. Central tendency Dispersion Dependency
Nominal Mode Frequency
Ordinal Median,
Percentile Interval of variation Spearman corr. coeff.
Kendall corr.coef.
Interval Mean Standard deviation, variance and range Pearson corr.coeff.
Ratio Geometric mean Coefficient of variations
Data visualization: ...

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