3. Justify why type of data and scale of measurement is important

Transcription

1 TYPES OF DATA OBJECTIVE: 1. Identify how and why data differs 2. Classify data obtained from various variables 3. Justify why type of data and scale of measurement is important TARGET: STA151, STA151, STA161, PYC374, any other modules using types of data and scale of measurement. WHY study type of data and scale of measurement? EXAMPLES OF DATA Example 1 Stones Example 2 Example 3 Example 4 Different sizes of UNISA T-shirts (Large, Medium, Small) 414 SMS sent out for workshop, 15 responses 1 students weight in kg Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 1

2 What is the difference between the 4 examples of data? The differences between the data can be explained by the following algorithm. ALGORITHM: TYPES OF DATA Qualitative Names / categories quality Quantitative Numeric / numbers quantity XS, S, L, XL XXL Discrete Number of Counting (How many ) Continuous Unit of Measurement (How much, far or high...) Qualitative sounds like quality. Words are used to describe quality (Example 1 and 2 of data). Hence, qualitative data come from variables that use words to describe categories. Do not be fooled! Numerical numbers can also be used to describe categories. For example, the numbers on soccer Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 2

3 players jerseys identify the position that someone plays. The role that the number plays is really that of a name, word or category in this situation. Quantitative sounds like quantity. Numbers are used to describe quantity (Example 3 and 4 of data). Quantitative data can be described in terms of how many... and how much... where the response is some quantity. How many... indicates that counting is taking place. The data produced is described as quantitative discrete data, visually represented by dots. Why use dots? The dots are used to represent the outcome of the discrete data. The outcome is a whole number {, 1, 2, 3,...}. How much..., how far... or how high... indicate that measurement is taking place. The data produced is described in these situations as quantitative continuous data, visually represented by a number line between two end points. Why this representation? This data can be any real number ( ). This means this data could have whole numbers and/or numbers with decimal places. In a frequency distribution table this data would be represented by class intervals, with class boundaries at the beginning and end of each class interval. Another property worth noting is that these quantities have some unit of measurement. kilometres (km) Feet (ft) kilograms (kg) litres (l) seconds (sec), degrees of Celsius ( C) dollars ($) metre (m) hours (hr) grams (g) Years (yr) Rands (R), degrees of Fahrenheit ( F) cents (c) millimetres (mm) Insert your own examples in the blank squares above? SCALE OF MEASUREMENT The activities in this section have been designed to show how variables can produce different types of data and the characteristic that is measured will give different scales of measurement. A student was asked to take Example 1 of data, the stones, and sort them into categories according to his/her criteria of choice. Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 3

4 What criteria would you have used to sort them into categories? THE STONES What criteria did the student use? THE OUTCOME Did you have difficulty answering the above question? The student was initially using colour, then decide to include size. When sorting the stones on both colour and size, the categories become diluted. In other words, there will be many categories with too few stones in each category. It is possible to do this. But this will largely be determined by your sample size, the number of stones you have to categorize. 11 CATEGORIES SORTED BY COLOUR AND SIZE Quantitative Literacy (QL) UNISA Durban Learning Centre, 4

5 EXAMPLE 1 BY COLOUR A second student sorted the stones by colour only. This is the outcome. 5 CATOGRIES SORT BY COLOUR Colour Tallies Frequency Brown 4 Black 2 Nominal Grey 8 White 4 Stone 1 total 19 Sorting the stones by colour gave a nominal scale of measurement. A nominal scale names the categories of data. What is the mode of this data? If the answer was 4, then you have misunderstood the definition of the mode. Definition: The mode is the data value which occurs the most often in a data set. In other words, it has the highest frequency. Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 5

6 The data looks like this {brown; brown; brown; brown; black; black; grey; grey; grey; grey; grey; grey; grey; grey; white; white; white; white; stone} Grey occurs most frequently. Hence, the mode of the data is grey. EXAMPLE 1 BY SIZE A third student sorted the stones by the size criteria. The outcome was as follows: 5 CATEGORIES SORT BY SIZE Colour Tallies Frequency XS (extra small) 6 S (small) 2 Ordinal M (medium) 4 L (large) 5 XL (extra-large) 2 total 19 Sorting the stones by size gave an ordinal scale of measurement. An ordinal scale names the categories of data and now there is order in the categories. There is distinctly a magnitude relationship of less than or greater than between the categories. Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 6

7 What is the mode of this data? It is XS. Beware that the word SIZE can take on different meanings when used as a variable. Note the differences in the two examples below Qualitative, ordinal data T-shirt sizes Quantitative, continuous data The size of the garden patch is 2m 2 It is important to READ each sentence clearly, and look at words in the context of the sentence or variable. EXAMPLE 1 BY SIZE (in mm) The size (in mm) of longest side of each stone is given in the following table. 18mm 13mm 21mm 12mm 24mm 2mm 6mm 55mm 53mm 49mm 47mm 36mm 34mm 3mm 29mm 44mm 37mm 45mm 36mm What is the mode of this data? From the data 36 mm occurs most often, hence the mode is 36mm. Note that this data s unit of measurement is mm. There was some form of action of measurement. According to the types of data algorithm above, this data is quantitative, continuous data. Size has been measured in this situation. The smallest data value is 12mm and the largest data value is 6mm. Begin the first class interval at 1mm with 1mm class width. The results are as follows: Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 7

8 FREQUENCY DISTRIBUTION TABLE Important to Note: The stone example can be qualitative or quantitative data. The type of data depends on how we chose to measure the data. Be aware of this! CONVERSION FORMULAS From Celsius to Fahrenheit 9 C 32 F (1) 5 From Fahrenheit to Celsius 5 F 32 C (2) 9 Substitute C into the formula (1). What is the outcome? Substitute F into the formula (2). What is the outcome? What can you conclude? Solution: Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 8

9 C F substitute F 5 C F 32 5 C 9 substitute F C C The zero is not an absolute zero point, in other words, the zero does not mean that no temperature exists. As C 32 F and F 17.8 C. This scale of measurement is known as Interval scale. It has a magnitude relationship of less than or greater than quality that ordinal scale possess. Interval scale has an additional scale quality of equal intervals. For example, the difference between 1 C. 17 C and 18 C is However, it is not possible to compare 15 C and 3 C. Note that Multiples are therefore meaningless. SCALE USED MOSTLY IN STATISTICAL ANALYSIS 1 C ; between Ratio scale has a absolute zero point where zero has a meaning. For example Distance: it would mean no distance, i.e. stationary. Height: it would mean no height Rands (R): No money Age: no age Ratio scale has all four qualities of the former scales. Namely, it categorizes, has a magnitude relationship or orders data, equal intervals, has an absolute zero point. 18 C and 3 C is not twice as hot as 19 C is 15 C. Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 9

10 Ratio scale data comes from Quantitative data that discrete (counting) continuous (unit of measurement) WHY study type of data and scale of measurement? The type of data determines the scale of measurement. Scale of measurement determines the type of statistical analysis Statistical analysis Scale of Measurement Type of Data Quantitative Literacy (QL) UNISA Durban Learning Centre, 1

11 SCALE OF MEASUREMENT: Nominal Ordinal Interval Ratio Type of data Qualitative Qualitative Quantitative Quantitative Attribute Names the attributes Ranks the attributes Ranks the attributes Ranks the attributes Absolute zero meaningless meaningless meaningless meaningful Multiples - - meaningless meaningful Frequency Yes of categories Yes of categories Yes of intervals /bins / class intervals Percentage Categories Categories Classes or intervals Yes of intervals / bins / class intervals Classes or intervals Mode Yes Yes Yes Yes Median No No Yes Yes Mean No No Yes Yes Graphical displays Pie chart Bar chart Pie charts Bar charts Stem-and-leaf Cross tabulation Histograms Scatter plots Examples Brands of toothpaste (Aquafresh, Colgate, Close up, Mcleans, Mentadent P, Sensodyne) Size (XS, S, M, L, XL, XXL) Temperature (Celsius - C, Fahrenheit - F ) Distance or weight usually have some sort of measurement scale Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 11

12 EXERCISE: Classify the data obtained from each of the following variables Type Data (qualitative, discrete or continuous) Scale of Measurement (nominal, ordinal, interval or ratio) The excel spreadsheet called types of data.xls is an interactive approach. It pops up green if the answer is correct. No Variable Type Data Your status as a full-time or part-time student Would your overall rating of the restaurant be excellent, good, fair or poor? What is the approximate distance of UNISA from your home? The weight of a new born baby The types of modules available to study The time (in months) before a box of long-life milk expires The temperature at noon (12h) each day Level of education The number of employees attending the annual staff meeting The time that a student spends to complete an assignment Your gender status The winning time for a horse running in a Derby A patient expresses the amount of pain he/she feels on a 1 point scale where 1 is no pain and 1 means extreme pain The size of a factory in metres squared The number of mice used in a maze experiment Satisfaction levels of brand (very satisfied, satisfied, neither nor, dissatisfied, very dissatisfied) The names of students attending a tutorial The most frequent use of your microwave oven (reheating, defrosting, warming, other) Scale of Measurement Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 12

13 The letter grades received by students in a statistics class The kind of tile fitted to the bathroom floor of a townhouse The jersey numbers on the SA rugby team The height of a newly planted fruit tree (in mm) Agreement levels of the difficulty of doing statistics (Strongly agree, agree, neither nor, disagree, strongly disagree ) The distance a person walks to catch a taxi The Chemistry, Physics, Mathematics and Statistics department Military ranking The average mark a learner obtains in a class test Whether a student does poor, fair or good in an assignment How high do kangaroos jump? How many South Africans citizens live in KZN? Rating by students of the teaching ability of five professors Number of no-shows for a airline flight Make of car that employees of a company drive The amount of your student loan Which one of the attributes of the restaurant to you find most attractive: service, prices, quality of food, image or a varied menu? How many occasions have you eaten at a restaurant previously? Have you eaten at Ocean Basket in the past month? Marital status How many people refused to answer a survey Classification of rock types The number of blogs you view per week The score obtained on a psychometric test Age of a person Are you male or female? The number of rings on a person s finger Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 13

14 Acceleration time of a motor car The number of cars passing the intersection A person s opinion about legalization of marijuana (strongly agree, agree, neither nor, disagree, strongly disagree) Number of people aboard a commercial airplane Acceleration speed of a motorbike REFERENCES KATE STRYDOM strydks@unisa.ac.za 212 Quantitative Literacy (QL) UNISA Durban Learning Centre, strydks@unisa.ac.za 14