What is the level of measurement that consists of classifying data into categories in which order is the only identifying element?
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Applied Statistics - Lesson 1Lesson Overview
The last half of the course will cover inferential statistics. Show
General Terms Used Throughout Statistics
The term population will vary widely with its application. Examples could be any of the following proper subsets: animals; primates; human beings; homo sapiens; U.S. citizens; who are attending Andrews University, as graduate students, in the School of Education, as Masters students, female, last name starting with S, who web registered.
How samples are obtained or types of sampling will be studied in lesson 7. Most any of the examples above for population could serve as a sample for the next higher level data set.
The plural of statistic just above is another basic meaning of statistics. Assume there are 8 students in a particular statistics class, with 1 student being male. Since 1 is 12.5% of 8, we can say 13% are male. The 13% represents a parameter (not a statistic) of the class because it is based on the entire population. If we assume this class is representative of all classes, and we treat this 1 student as a sample drawn from a larger population, then the 13% becomes a statistic.
Inferential statistics is used to draw conclusions about a population by studying a sample. It is not guesswork! We test hypotheses about a parameter's value with a certain risk of being wrong. That risk is carefully specified. Also, descriptive and inferential statistics are not mutually exclusive. The inferences made about a population from a sample help describe that population. We also tend to use Roman letters for statistics and Greek letters for parameters. Basic Mathematics for StatisticsThis course will avoid complex models utilizing complicated mathematics. You will need to be familiar with, however, the fundamental arithmetic operations, elementary algebra, and some basic symbolism.An interesting subset of the natural numbers generated by addition are called Triangular Numbers. These are so called because these are the total number of dots, if we arrange the dots in a triangle with one additional dot in each layer.
Suppose we wish to add together the first 100 natural numbers, which is equivalent to finding the 100th triangular number. One way to do this is by grouping them as follows:
In general we write: where mathematicians use the capital Greek letter (sigma) to represent summation. Your teacher has a particular fondness for this symbol since the first computer he had much access to had that nickname.There are three important rules for using the summation operator:
Exponentiation is a general term which includes squaring (122=144), cubing (63=216), and square roots (16½= (16)=4. When the square root symbol (surd and symbol of inclusion, in recent history a vinculum, but historically parentheses) is used, we general (although not quite always) mean only the positive square root.The absolute value operator indicates the distance (always non-negative) a number is from the origin (zero). The symbol used is a vertical line on either side of the operand. Thus, if x>0, then |x|=x, if x<0, then |x|=-x, and if x=0, |x|=0. (x2)=|x|.There is a proscribed order for arithmetic operations to be performed. Example: If we write 4 × 5 + 3 it is conventional to multiply the 4 and 5 together before adding the 3 and thus obtain 23. Some calculators are algebraic and handle this appropriately, others do not. Parentheses and other symbols of inclusion are used to modify the normal order of operations. We say these symbols of inclusion have the highest priority or precidence. Exponentiation is done next. There is confusion when exponents are stacked which we will not deal with here except to say computer scientists tend to do it from left to right while mathematicians know that is wrong. Multiplication and Division are done next, in order, from left to right. Addition and Subtraction are done next, in order, from left to right. A mnemonic such as Please Eat Miss Daisy's Apple Sauce can be useful for remembering the proper order of operation. Accuracy vs. PrecisionThe distinction between accuracy and precision, reviewed in Numbers lesson 9, is very important.This ties in with significant figures, and proper rounding of results. I have several major concerns regarding significant digits.
Uses and Abuses of StatisticsMost of the time, samples are used to infer something (draw conclusions) about the population. If an experiment or study was done cautiously and results were interpreted without bias, then the conclusions would be accurate. However, occasionally the conclusions are inaccurate or inaccurately portrayed for the following reasons:
Types of DataA dictionary defines data as facts or figures from which conclusions may be drawn. Thus, technically, it is a collective, or plural noun. Some recent dictionaries acknowledge popular usage of the word data with a singular verb. However we intend to adhere to the traditional "English" teacher mentality in our grammar usage—sorry if "data are" just doesn't sound quite right! (My mother and step-mother were both English teachers, so clearly no offense is intended above.) Datum is the singular form of the noun data. Data can be classified as either numeric or nonnumeric. Specific terms are used as follows:
The structure and nature of data will greatly affect our choice of analysis method. By structure we are referring to the fact that, for example, the data might be pairs of measurements. Consider the legend of Galileo dropping weights from the leaning tower of Pisa. The times for each item would be paired with the mass (and surface area) of the item. Something which Galileo clearly did was measure the time it took a pendulum to swing with various amplitudes. (Galileo Galilei is considered a founder of the experimental method.) Levels of MeasurementThe experimental (scientific) method depends on physically measuring things. The concept of measurement has been developed in conjunction with the concepts of numbers and units of measurement. Statisticians categorize measurements according to levels. Each level corresponds to how this measurement can be treated mathematically.
Nominal comes from the Latin root nomen meaning name. Nomenclature, nominative, and nominee are related words. Gender is nominal. (Gender is something you are born with, whereas sex is something you should get a license for.) Example 1: Colors To an electronics student familiar with color-coded resistors, this data is in ascending order and thus represents at least ordinal data. To a physicist, the colors: red, orange, yellow, green, blue, and violet correspond to specific wavelengths of light and would be an example of ratio data. Example 2: Temperatures Only Kelvin and Rankine have true zeroes (starting point) and ratios can be found. Celsius and Fahrenheit are interval data; certainly order is important and intervals are meaningful. However, a 180° dashboard is not twice as hot as the 90° outside temperature (Fahrenheit assumed)! Rankine has the same size degree as Fahrenheit but is rarely used. To interconvert Fahrenheit and Celsius, see Numbers lesson 12. (Note that since 1967, the use of the degree symbol on tempertures Kelvin is no longer proper.) Although ordinal data should not be used for calculations, it is not uncommon to find averages formed from data collected which represented Strongly Disagree, ..., Strongly Agree! Also, averages of nominal data (zip codes, social security numbers) is rather meaningless!
What level of measurement that is used to classify or categorize data?The researcher should note that among these levels of measurement, the nominal level is simply used to classify data, whereas the levels of measurement described by the interval level and the ratio level are much more exact.
Is the level of measurement where data are classified into categories and the order of those categories is not important?In a nominal level variable, values are grouped into categories that have no meaningful order. For example, gender and political affiliation are nominal level variables.
Which level of measurement consists of categories only where data Cannot be arranged in an ordering scheme?Nominal - data consists of names, labels or categories only. The data cannot be arranged in an ordering scheme (such as low to high).
What do you call the level of measurement that classifies data into categories and can be ranked?In scientific research, a variable is anything that can take on different values across your data set (e.g., height or test scores). There are 4 levels of measurement: Nominal: the data can only be categorized. Ordinal: the data can be categorized and ranked.
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