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# Probability Plot, Sample Size, ANOVA, & Regression

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1. What are the four levels of measurement scales? Give examples of each and explain in detail.

2. Explain the use of normal probability plot to evaluate whether a set of data is normally distributed? Please discuss in detail.

3. Discuss how a sample size, n, an increase in confidence is achieved by widening the confidence interval.

4. With regard to hypothesis testing about two means, what is the distinction between two independent populations and two related populations? Please be specific in your answer.

5. Discuss the assumptions of ANOVA? Please list and elaborate on each answer.

6. Explain the null hypothesis (Ho) for a simple linear regression equation? Please list and explain in detail.

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The solution determines what the four level of measurement scales are and gives examples of each.

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1. What are the four levels of measurement scales? Give examples of each and explain
in detail.

The four levels of measurement scales are (1) nominal (2) ordinal (3) interval
and, (4) ratio level.
Nominal scales produce qualitative measurement variables, while ordinal, interval, and ratio scales produce quantitative measurements variables.

Nominal-Level measurement :
Nominal-level measurement is the most basic level of measurement, in which the things being measured are simply classified into unique categories. These categories are mutually exclusive( no things can be placed in more than one category ) and totally inclusive( every thing can be placed in at least one category ). Categories on nominal scales are not ordered in any way( e.g., from small to large ), and numbers are used only as labels for categories. The minimum number of categories on a nominal scale is two and there can be as many categories as needed. Examples of nominal scales are, type of fish ( e.g., shark, flounder, trout ), presence or absence of disease (e.g., absence = 0, presence = 1).

Ordinal-Level measurement :
Ordinal-level measurement is the next level above nominal. Its scales retain the nominal level property of classifying things into one and only one category, but now the categories are ordered (ranked according to the magnitude of the characteristic being measured ). Each category can now be said to be greater than (>) or less than (<) its neighbor, depending on the amount of the characteristic it represents.
Some examples of ordinal scales are, ranking the size of a set of objects on a three-number scale (1 = small, 2 = medium, 3 = large ). Ranking the economic conditions of different sections of a society on a five-number scale ( from 1 = very bad to 5 = excellent). Ordinal measurement can indicate only the relative amount of a characteristic in each thing being measured, but not exactly how much more of the characteristic one thing has versus another.

Interval-Level measurement :
Interval-level is the next higher level of measurement above ordinal level. Its scales include the properties of nominal ( = , ≠ ) and ordinal (< , >) scales, and in addition have uniform and standard reference units. Such units eliminate subjectivity in quantitative measurements, producing scales with constant and equal intervals.
One example of an interval scale is Celsius (or centigrade ) scale for temperature. On this scale, zero temperature (0oC) is arbitrarily defined as the freezing point of water, and the unit (oC) is then defined as 1/100th of the distance on the scale to the ...

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