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Statistik topic1 types of data


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  • 1. Topic 1 Types of Data LEARNING OUTCOMES By the end of this topic, you should be able to: 1. differentiate Qualitative and Quantitative data; 2. distinguish nominal and ordinal (as well as level of achievement and ranking); and 3. discriminate between discrete and continuous data. INTRODUCTIONGenerally, every study or research will generate data set of various types. In thistopic, you will be introduced to two data classifications namely Qualitative andQuantitative. The qualitative data can further be classified into nominal andordinal data. The quantitative data can be further classified as discrete andcontinuous data. It is important to understand these classifications so that you canmodify the raw data wisely to suit the objective of data analysis.1.1 DATA CLASSIFICATIONA set of data consists of measurements or observations of a certain criteriaconducted on a group of individuals, or objects or items. A variable is an interested criterion to be measured on each individual such as height, or weight; or a criterion to be observed such as one’s ethnic background or intelligent quota.It is called variable because its value varies from one individual to another in thesample. Depending on the objective of a research, there could be more than one
  • 2. 2 TOPIC 1 TYPE OF DATAvariable being measured or observed on each individual. For example, aresearcher may want to observe the following variables on five individualsconsisting of 2 females and 3 males from a Primary School in State J. Theobtained data are given in Table 1.1. Table 1.1: A Set of Data Consists of 5 Variables Measured on Each Individual Number of PMR Weight Father’s Individual Ethnic Sisters in Grade- Achievement (Kg) Qualification Family English 1 Malay 3 20 Degree A Excellent 2 Chinese 2 23 Diploma A Excellent 3 Malay 4 25 STPM C Ordinary 4 Indian 5 19 PMR B Good 5 Chinese 1 21 SPM D Poor By examining Table 1.1: (a) Can you observe the different types of variables and their respective values? (b) Can you see that value of each variable varies from individual 1 to individual 5?A variable which possesses numerical value like weight, is termed asQuantitative Variable.It is further classified into Discrete Quantitative Variable and ContinuousQuantitative Variable:(i) The value of Discrete Quantitative Variable is integer by nature. Usually the value is obtained through counting process. The number of sisters in a family is an example of Discrete Quantitative Variable.(ii) On the other hand, the value of Continuous Quantitative Variable is obtained through a measuring process. The height of pupil is an example of Continuous Quantitative Variable.There is another type of variable whose value is non-numerical in nature such asEthnic Background of pupil in school. This type of variable is called QualitativeVariable. In the Malaysian context, the values of variable ethnic background, are
  • 3. TOPIC 1 TYPE OF DATA 3Malays, Chinese, Indian and others. The nature of the value is just categoricaland does not involve counting or measuring process to get the value.The categorical value can be in either of Nominal form such as Ethnicity, orOrdinal form such as PMR English Grade. Thus Qualitative Variable can befurther classified into Nominal Variable and Ordinal Variable. The ordinalvariable can be further classified into Categorical Level or Ordered Categoricalsuch as Achievement, and Categorical Rank such as Academic Qualification.Figure 1.1 below depicts the classification of variables. Figure 1.1: Classification of variables1.2 NOMINAL DATA The word Nominal is just the name of a category and contains no numerical value. The variable cannot be measured or counted and the values neither can be arranged in sequence nor in order. In data analysis, this variable will be represented by “code number” to differentiate the categorical values of the variable.
  • 4. 4 TOPIC 1 TYPE OF DATAFor example for the variable Gender, ‘0’ will represent ‘Male’, and ‘1’ willrepresent ‘Female’. For variable ‘State’, ‘01’ will represent ‘Johor State’, ‘08’ willrepresent ‘Perak State’ etc. Any integer can be the “code number” but itsrepresentation must be defined clearly. It is important to note that the ‘codenumber’ is just ‘categorised representation’ which does not carry numerical value.This means that although by nature number 0 is less than 1 but we cannot say thatcode ‘0’ is less than code ‘1’ which can further mislead and wrongly order thatcategory ‘Male’ is “less than” ‘Female’.Table 1.2 presents examples of Nominal Variable with their values. In this table,the last column shows examples of code numbers which are commonly used byresearcher. When we key in data into the computer, data entry will type 0 forMale individual, and type 1 for female individual. The computer will then countcode ‘0’ to give the frequency of Male individual, and count code ‘1’ to give thefrequency of Female individual. Similar process will be done for other nominalvariables. We can convert the frequency into percentage as required. In the dataanalysis, this process is called cross tabulation whereby descriptive statistics suchas min, median or mode of each category can be obtained. Table 1.2: Example of Nominal Data Nominal Variable Values Numerical Code Gender Male 0 Female 1 Religion Islam 1 Christian 2 Hindu 3 Budha 4 Others 5 Ethnic Malay 1 Chinese 2 Indian 3 Others 4 Marital Status Single 1 Married 2 Widow 3 Widower 4 Agreement Yes 0 No 1
  • 5. TOPIC 1 TYPE OF DATA 5You are encouraged to answer the following exercise to test whether youunderstand the concept. ACTIVITY 1.1 Give the code number to represent the given categorical value of the following Nominal Variables: (a) state of origin (b) month of birth (c) the degree you obtained. Can all data be classified as Nominal Data? Suppose you are going to use a data comprised of code numbers representing individual’s perception on a certain opinion. Is this data still considered as nominal data? Give your reasoning.1.3 ORDINAL DATAOrdinal Data such as Achievement in Table 1.1 is a qualitative data whosecategorical values can be arranged according to some ordered value. However thedistance between any two values is not known and cannot be measured. No oneknows the distance between poor and good as well as between poor and excellent.There are two types of Ordinal Data namely level or degree such as variableAchievement and rank such as Father’s Academic Qualification as mentioned inTable 1.1. Likert Scale is synonyms with rank Ordinal Data. The scale uses sequence of integers with fixed interval such as 1,2,3,4,5 or perhaps 1,3,5,7,9. There is no standard rule in choosing the integers.A researcher can take 10, 20, 30, 40, 50, or even 100, 200, 300, 400, etc.However, in practice, it is common to choose small integers. The sequence ofintegers is used to represent the corresponding order of categorical values. Thus, itis important to define clearly such representation.
  • 6. 6 TOPIC 1 TYPE OF DATAAs for example, consider a simple experiment of ranking the taste of several typesof ice-cream by respondent. Scale ‘1’ could represent ‘very tasty’, ‘2’ to represent‘tasty’, ‘3’ to represent ‘less tasty’, ‘4’ to represent ‘not tasty’, and ‘5’ to represent‘not at all tasty’. The values of taste perception is by nature of rank order whichbegins with the highest degree represented by scale 1 and the descending degreesto the lowest which is represented by scale 5. However, one can reverse the orderof integer values to make it in line with the order of the categorical values i.e.scale ‘5’ can represent ‘very tasty’, and scale ‘1’ will represent ‘not at all tasty’.Again here, in the previous representation, although we have equal interval ‘5-4-3-2-1’, but it does not represent equal difference in the respected degree ofperception.Table 1.3 depicts several types of Level or Degree Ordinal Data. Table 1.3: Examples of Level or Degree Ordinal Data Variable Categorical values Likert Scale Perception Level Very tasty 5 Tasty 4 Less Tasty 3 Not tasty 2 Not tasty at all 1 Satisfaction Level Very satisfactory 5 Satisfactory 4 Moderately satisfactory 3 Un-satisfactory 2 Very Un-satisfactory 1 Degree of Strongly Agree 5 Agreement Agree 4 Doesn’t Matter 3 Disagree 2 Strongly disagree 1 Level of Excellent 5 Achievement Very Good 4 Good 3 Satisfactory 2 Fail 1In the case of Rank Ordinal Data, the categorical values can be arranged in orderfrom the highest level going down to the lowest level or vice-versa. Table 1.4presents various forms of Rank Ordinal Data. You can see that the value of eachvariable is arranged from the highest to the lowest level. For Grade of Hotel, wehave grade 5*, then 4* and so on, until the last grade 1*.
  • 7. TOPIC 1 TYPE OF DATA 7 Table 1.4: Examples of Rank Ordinal Data Variable Rank Categorical Grade of Hotel 5* 4* 3* 2* 1* Grade of Examination A B C D E Teacher’s Qualification Degree Diploma STPM SPMRank of Teachers’ Profession Head Master Senior Assistant Teacher Attachment Teacher ACTIVITY 1.2Give the code number to represent the categorical value of the followingNominal Data:(a) Degree of severe-ness in injury.(b) Class of a degree obtained.(c) Level of delivery of a lecture by lecturer.
  • 8. 8 TOPIC 1 TYPE OF DATA1.4 DISCRETE DATADiscrete Data is the one that consist of integers or whole numbers. This type ofdata can easily be obtained through counting process. The followings areexamples of discrete data: The number of stolen cars every month, in 2006. The number of students absent in a class every month in 2005. The number of rainy-days in a year. The number of children in a family for 50 families. The number of students who obtained grade A in a final examination.Researcher can obtain the mean, mode, median and variance of discrete data.However, the values of these statistics may no longer be integer. Give other examples of discrete data. You may discuss with your course mates. ACTIVITY 1.3 What are the criteria of Discrete Data?1.5 CONTINUOUS DATAContinuous Data is the value of continuous variable that consist of numberswith decimals. This data usually can be obtained through a measuring process.The following are examples of continuous variables: Height, weight, age. Temperature, pressure. Volume, mass, density. Time, length, breadth.One can obtain mean, mode, median, variance and other descriptive statistics of adata set which will be discussed in Topic 2.
  • 9. TOPIC 1 TYPE OF DATA 9 ACTIVITY 1.41. What are the criteria of a continuous random variable?2. For the following observations, state whether the concerned variable is categorical or numerical type. Data Variable (a) The age of employees in an electronic factory (b) Rank of army officer (c) The weight of new born baby (d) Household income (e) Rate of death in a big city (f) The number of students in each class at a school (g) Brands of television found in market3. For the following observations, state whether the concerned variable is discrete or continuous. Data Variable (a) The time spent by children watching television (b) Rate death caused by homicide (c) The number of criminal cases in a month (d) The price of terrace house in KL (e) The number of patients over 65 years old (f) The rate of unemployment in Malaysia4. Classify the following observations whether the variables concerned are either Nominal or Ordinal types. For Ordinal Type, please classify further to either level or degree Ordinal, or Rank Ordinal. Level Rank Data Nominal Ordinal Ordinal (a) Brands of computer owned by student (IBM, Acer, Compaq, Dell, Others) (b) Quality of books published by university (Good, Satisfactory, Moderate, Unsatisfactory, Bad) (c) Category of houses (High cost, Moderate Cost, Low Cost) (d) Level of English Competency at school (Excellent, Good, Moderate, Satisfactory, Unsatisfactory, Very Poor) (e) Types of daily News Paper read (Berita Harian, Utusan Malaysia, Star, New Straits Times)
  • 10. 10 TOPIC 1 TYPE OF DATAA variable is observable or measurable criteria of individuals in a sample. It canbe qualitative or quantitative. Quantitative variable can be of discrete naturewhose values are integer obtained through a counting process. Qualitative variablecan be classified into Nominal and Ordinal. The ordinal variable can further besub-classified into level or degree ordinal and Rank Ordinal. The variable also canbe continuous whose values are numbers with decimals obtained throughmeasuring process. On the other hand, a qualitative variable consists ofcategorical data which is non-numerical in nature. In research, qualitative datawill be represented by defined code number which cannot be used in arithmeticaloperation.