Section 1-2 Variables and types of Data

Objective 3: Identify types of Data In this section we will detail the types of data and nature of variables.

1-2 Variables and Types of Data Data Qualitative Categorical Quantitative Numerical, Can be ranked Discrete Countable 5, 29, 8000, etc. Continuous Can be decimals 2.59, 312.1, etc. 4 Bluman Chapter 1

Data QualitativeQuantitative DiscreteContinuous

Qualitative variables Are variables that can be placed into distinct categories, according to some characteristic or attribute such as: Gender Political affiliation Grade level Are variables that can be placed into distinct categories, according to some characteristic or attribute such as: Gender Political affiliation Grade level

Quantitative variables Are numerical and can be ordered or ranked. For example: Age height weight Are numerical and can be ordered or ranked. For example: Age height weight

Discrete variables Assumes values that can be counted. For example: Number of coffee shops in NoPo. Number of turkeys your mama is going to cook on Thanksgiving. Number of unwanted hair on your chin. Assumes values that can be counted. For example: Number of coffee shops in NoPo. Number of turkeys your mama is going to cook on Thanksgiving. Number of unwanted hair on your chin.

Continuous variables Result from a measurement and can take on infinite number of values, including decimal. For example: Temperature of a fully cooked turkey.. Weigh of a turkey Ounces of gravy on mashed potatoes. Result from a measurement and can take on infinite number of values, including decimal. For example: Temperature of a fully cooked turkey.. Weigh of a turkey Ounces of gravy on mashed potatoes.

Rounding Continuous data is rounded. Continuous data is usually rounded to the nearest given unit. Raw data and boundaries Continuous data is rounded. Continuous data is usually rounded to the nearest given unit. Raw data and boundaries

1-2 Recorded Values and Boundaries VariableRecorded ValueBoundaries Length15 centimeters (cm) Temperature 86  Fahrenheit (  F) Time0.43 second (sec) Mass1.6 grams (g) cm  F sec g 11 Bluman Chapter 1

About Boundaries Boundaries always have one more decimal place than the data. Boundaries always end in a 5. We will cover boundaries further in chapter 2. Boundaries always have one more decimal place than the data. Boundaries always end in a 5. We will cover boundaries further in chapter 2.

Levels of measure Nominal Ordinal Interval Ratio Examples Page 8

Nominal Nominal – categorical (names)  When measuring using a nominal scale, one simply names or categorizes responses. Gender, handedness, favorite color, and religion are examples of variables measured on a nominal scale.  The essential point about nominal scales is that they do not imply any ordering among the responses. For example, when classifying people according to their favorite color, there is no sense in which green is placed "ahead of" blue.  Responses are merely categorized. Nominal scales embody the lowest level of measurement. 14 Bluman Chapter 1

Ordinal Ordinal – nominal, plus can be ranked (order)  A researcher wishing to measure consumers' satisfaction with their microwave ovens might ask them to specify their feelings as either "very dissatisfied," "somewhat dissatisfied," "somewhat satisfied," or "very satisfied." The items in this scale are ordered, ranging from least to most.  This is what distinguishes ordinal from nominal scales. Unlike nominal scales, ordinal scales allow comparisons, ranking or “ordering” 15 Bluman Chapter 1

Interval Interval – ordinal, plus intervals are consistent Interval scales are numerical scales in which intervals have the same interpretation throughout. Interval scales are not perfect, however. In particular, they do not have a true zero point even if one of the scaled values happens to carry the name "zero." 16 Bluman Chapter 1

Ratio Ratio – interval, plus ratios are consistent, true zero  The ratio scale of measurement is the most informative scale. It is an interval scale with the additional property that its zero position indicates the absence of the quantity being measured.  You can think of a ratio scale as the three earlier scales rolled up in one. Like a nominal scale, it provides a name or category for each object (the numbers serve as labels). Like an ordinal scale, the objects are ordered (in terms of the ordering of the numbers). Like an interval scale, the same difference at two places on the scale has the same meaning. And in addition, the same ratio at two places on the scale also carries the same meaning. 17 Bluman Chapter 1

Consequences of level of measurement Why are we so interested in the type of scale that measures a dependent variable? The crux of the matter is the relationship between the variable's level of measurement and the statistics that can be meaningfully computed with that variable. Bluman Chapter 118

Let's practice The website above also some more examples and explanation of what we just covered. Bluman Chapter 119

1-2 Variables and Types of Data Determine the measurement level. VariableNominalOrdinalIntervalRatioLevel Hair ColorYesNoNominal Zip CodeYesNoNominal LetterGradeYes NoOrdinal ACT ScoreYes NoInterval HeightYes Ratio AgeYes Ratio Temperature(F)Yes NoInterval 20 Bluman Chapter 1

On your own Study the examples listed on table 1-2 on page 8. Do applying concepts on page 9 And answer questions 1-10 on page 26. Bluman Chapter 121