<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">The way a set of data is measured is called its&nbsp;<strong>level of measurement</strong>. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statistical operation can be used with every set of data. Data can be classified into four levels of measurement. They are (from lowest to highest level):</span></span></p>

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<ul>
	<li style="text-align:justify">
	<p><span style="font-size:14px"><span style="color:#424242">Nominal scale level</span></span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px"><span style="color:#424242">Ordinal scale level</span></span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px"><span style="color:#424242">Interval scale level</span></span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px"><span style="color:#424242">Ratio scale level</span></span></p>
	</li>
</ul>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Data that is measured using a&nbsp;<strong>nominal scale</strong>&nbsp;is&nbsp;<strong>qualitative (categorical)</strong>. Categories, colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data. Nominal scale data are not ordered. For example, trying to classify people according to their favorite food does not make any sense. Putting pizza first and sushi second is not meaningful</span><span style="color:#424242">.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Smartphone companies are another example of nominal scale data. The data are the names of the companies that make smartphones, but there is no agreed upon order of these brands, even though people may have personal preferences. Nominal scale data cannot be used in calculations.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Data that is measured using an&nbsp;<strong>ordinal scale</strong>&nbsp;is similar to nominal scale data but there is a big difference. The ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks in the United States. The top five national parks in the United States can be ranked from one to five but we cannot measure differences between the data.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Another example of using the ordinal scale is a cruise survey where the responses to questions about the cruise are &ldquo;excellent,&rdquo; &ldquo;good,&rdquo; &ldquo;satisfactory,&rdquo; and &ldquo;unsatisfactory.&rdquo; These responses are ordered from the most desired response to the least desired. But the differences between two pieces of data cannot be measured. Like the nominal scale data, ordinal scale data cannot be used in calculations.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Data that is measured using the&nbsp;<strong>interval scale</strong>&nbsp;is similar to ordinal level data because it has a definite ordering but there is a difference between data. The differences between interval scale data can be measured though the data does not have a starting point.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Temperature scales like Celsius (C) and Fahrenheit (F) are measured by using the interval scale. In both temperature measurements, 40&deg; is equal to 100&deg; minus 60&deg;. Differences make sense. But 0 degrees does not because, in both scales, 0 is not the absolute lowest temperature. Temperatures like -10&deg; F and -15&deg; C exist and are colder than 0.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Interval level data can be used in calculations, but one type of comparison cannot be done. 80&deg; C is not four times as hot as 20&deg; C (nor is 80&deg; F four times as hot as 20&deg; F). There is no meaning to the ratio of 80 to 20 (or four to one).</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Data that is measured using the&nbsp;<strong>ratio scale</strong>&nbsp;takes care of the ratio problem and gives you the most information. Ratio scale data is like interval scale data, but it has a 0 point and ratios can be calculated. For example, four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points). The exams are machine-graded.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">The data can be put in order from lowest to highest: 20, 68, 80, 92.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">The differences between the data have meaning. The score 92 is more than the score 68 by 24 points. Ratios can be calculated. The smallest score is 0. So 80 is four times 20. The score of 80 is four times better than the score of 20.</span></span></p>