Data and scales of measurement
- 1. DATA AND SCALES OF MEASUREMENT PRESENTED BY : DR. RITU RANDAD FIRST YEAR MDS 1
- 2. CONTENTS • Introduction • What is DATA and SCALE? • Types of data • Types of scales • Measures of central tendencies • Conclusion • References 2
- 3. INTRODUCTION • In our daily life we are said to measure or calculate various information which determines weight, height or some other features of a physical object. We also measure when we judge how well we like a song, a painting or the personalities of people. • We thus measure physical objects as well as abstract concepts. It is easy to assign numbers in respect of properties of some objects, but it is relatively difficult in respect of others. Like measuring things as social conformity, intelligence or marital status. Fava GA, Tomba E, Sonino N ,Clinimetrics: the science of clinical measurements. 3
- 4. • Properties like weight , height etc can be measured directly with some standard of unit of measurement, but it is not easy to measure properties like motivation to succeed, ability to stand and so on. • To indicate a domain concerned with indexes, rating scales and other expressions that are used to describe or measured symptoms, physical signs and other clinical phenomena, we use various scales to measure them. 4 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition, New Delhi.
- 5. WHAT IS A MEASUREMENT? • Measurement is defined as a process of associating numbers or symbols to observations obtained in a research study. • These observations can be qualitative or quantitative. 5 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition, New Delhi.
- 6. WHAT IS DATA? • Data are individual pieces of information recorded and used for the purpose of analysis. • It is the raw information from which statistics are created. Statistics are the results of data analysis - its interpretation and presentation. 6 C R Kothari, Research Methodology methods and techniques, 3rd
- 7. • Data is distinct pieces of information, usually formatted in a special way. Data can exist in a variety of forms — as numbers or text on pieces of paper, as bits and bytes stored in electronic memory, or as facts stored in a person's mind. • Data is the plural of datum, a single piece of information. In practice, however, people use data as both the singular and plural form of the word, and as a mass noun. 7
- 8. • Data provides facts and figures from which conclusions can be drawn. • Data can relate to an enormous variety of aspects. 1. Weight and height recorded of students in a class. 2. Blood pressure and pulse rate recorded of patients in a medical opd. 3. Temperature of a city for a week. 8
- 9. • The data collected may be for profile or prospective studies at local, state, national or international levels. • Used to analyze changes in health or disease situations in community or population by standard parameters. Quantitative Qualitative 9 C R Kothari, Research Methodology methods and techniques, 3rd
- 10. QUANTITATIVE DATA • Quantitative Data: Data that can be measured with numbers, such as time, weight, number of participants, Number of defects, effort required to complete the task. It is called Numerical data. QUALITATIVE DATA • Qualitative data: Data can be represented by a name, symbol, or a number code. It is called Nonnumerical data that is usually textual and descriptive like female, most favorite, yes/no. 10 C R Kothari, Research Methodology methods and techniques, 3rd edition, Jaipur
- 11. QUALITATIVE DATA • There is no notion of magnitude or size of attribute, hence the presentation of frequency distribution is simple because the characteristic is not variable but discrete. • Classified by counting the individuals having same characteristic or attribute and not by measurement. • Only one variable is used. 11 C R Kothari, Research Methodology methods and techniques, 3rd
- 12. • Qualitative data also called as categorical data since this data can be grouped according to categories. • Qualitative data does not include numbers in its definition of traits. • Qualitative data is about the emotions or perceptions of people, what they feel. 12
- 13. 13 Qualitative data is important in determining the frequency of traits or characteristics. It allows the statistician or the researchers to form parameters through which larger data sets can be observed. Qualitative data provides the means by which observers can quantify the world around them.
- 14. METHODS OF COLLECTING QUALITATIVE DATA 1. One on one interview (face to face interview) 2. Focus groups 3. Record keeping 4. Process of observation 5. Longitudinal studies 6. Case studies 14
- 15. ADVANTAGES 1. In helps in depth information and analysis. 2. Rich data. 3. Understands what the customer/ patient thinks. DISADVANTAGES 1. Time consuming 2. Result depends on what researcher thinks. 3. Not easy to generalize. 15
- 16. QUANTITATIVE DATA • Quantitative data is defined as the value of data in the form of counts or numbers where each data-set has a unique numerical value associated with it. This data is any quantifiable information that can be used for mathematical calculations and statistical analysis, such that real-life decisions can be made based on these mathematical derivations. • This data can be verified and can also be conveniently evaluated using mathematical techniques. 16
- 17. • Quantitative data makes measuring various parameters controllable due to the ease of mathematical derivations they come with. Quantitative data is usually collected for statistical analysis using surveys, polls or questionnaires sent across to a specific section of a population. The retrieved results can be established across a population. 17
- 18. • Quantitative data is any quantifiable information that can be used for mathematical calculation or statistical analysis. This form of data helps in making real-life decisions based on mathematical derivations. • This data can be validated and verified. 18
- 19. QUANTITATIVE DATA • The data have a magnitude. • The characteristics is measured either on an interval or on ratio scale. • There are two variables : as height and frequency , eg: number of person with same characteristic and in same range. 19C R Kothari, Research Methodology methods and techniques, 3rd DISCRETE CONTINOUS
- 20. TYPES OF QUANTITATIVE DATA 1. Counter 2. Measurement of physical objects 3. Sensory calculations 4. Projection of data 5. Quantification of qualitative entities. Surveys and interviews are the main source to collect quantitative data. 20
- 21. ADVANTAGES 1. Conduct in depth interviews. 2. Minimal bias 3. Accurate results DISADVANTAGES 1. Resisted information 2. Depends on question types 21
- 23. DISCRETE DATA • Information that can be categorized into a classification. • Discrete data is based on counts. Only a finite number of value are possible, and the values that cannot be subdivided meaningfully. • Attribute data (discrete data) is data that can’t be broken down into a smaller unit and add additional meaning. It is typically things counted in whole numbers. There is no such thing as half a defect 23
- 24. CONTINUOUS DATA • Information that can be measured on a continuum or scale. Continuous data can have almost any numeric value and can be meaningfully subdivided into finer and finer increments, depending upon the precision of the measurement system. • Continuous data can be recorded at many different points (length, size, width, time, temperature, cost, etc.). • Continuous data is data that can be measured and broken down into smaller parts and still have meaning. Temperature and time, volume (like volume of water or air) and size are continuous data. 24
- 25. WHAT IS SCALE? • A scale is a tool or mechanism by which individual are distinguished as to how they differ from one another on the variables of interest to our study. • The scales of measurements can be considered in terms of their mathematical properties. • a) nominal scale • b) ordinal scale • c) interval scale • d) ratio scale 25 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition, New Delhi.
- 26. TYPES OF SCALES a) nominal scale b) ordinal scale c) interval scale d) ratio scale 26
- 27. 27
- 28. NOMINAL SCALE/ COUNTED DATA • Nominal scale is simply a system of assigning numbers or symbols to events in order to label them. • The numbers are just convenient labels for the particular class of events and as such have no quantitative value. • They help in keeping tracks of events, people and objects. 28 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition, New Delhi.
- 29. NOMINAL SCALE • Nominal data/scale is a type of data that is used to label variables without providing any quantitative value. Qualitative characteristics can be counted but not computed. 29 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th
- 30. • For recording the acquired data of marital status as 1,2,3 or 4 depending upon whether the person is single, married, widowed or divorced. • We can also record the characteristic has “yes or no” answers to question as “0” or “1”. 30 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th
- 31. • In the artificial or nominal way, categorical data can be made into numerical data , we refer these numbers we record as nominal data. • Nominal data is numerical in name only , because they don’t share any of the properties of numbers we deal in ordinary arithmetic. • The numbers used are just a convenient labels for the particular class of events and as such have no quantitative value. 31 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th
- 32. The nominal scale is the least powerful level of measurement. It indicates no order or distance relationship and no arithmetic origin. It simply describes the differences between things by assigning them to categories. They are widely used in surveys when data is being classified by major sub-groups of the population. Examples: - gender - race -whether or not tumor recurred 32 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition, New Delhi.
- 33. ORDINAL SCALE • The lowest level of the ordered scale that is commonly used . • This place events in order, but there is no attempt to make the intervals of scales equal in terms of rule. • They are generally used in research related to qualitative phenomena. • Ordinal data only permits the ranking of items from highest to lowest. 33 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition, New Delhi. Principles and practices of Biostatistics, B. Antonisamy, 10 July 2017, 7th edition.
- 34. ORDINAL SCALE • In situations when we can not do anything except set up inequalities, we refer to data as Ordinal data. • For example, one mineral can scratch another, it receives a higher hardness number on scale from 1 to 10. with this numbers we can write 5>2 or 6<9 , but we cannot write as 5-2 = 6-9. • The greater than symbol (>) in connection with ordinal data may be used to designated “happier than” or so on. 34 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition, New Delhi.
- 35. The use of ordinal data implies a statement of “greater than ” or “less than” without being able to state how much greater or less. The appropriate measure of central tendency is the median. They have no absolute values, and real differences between ranks may not be equal. 35
- 36. INTERVAL SCALE • The interval are adjusted in terms of rule that establishes on a basis for making the unit equal. • They have an arbitrary zero, but they are not possible to determine for an absolute zero or the unique origin. • The primary limitation is lack of true zero, it does not have a capacity to measure the complete absence of a trait or characteristic. 36 Principles and practices of Biostatistics, B. Antonisamy, 10 July 2017, 7th edition.
- 37. INTERVAL DATA • Interval data, also called an integer, is defined as a data type which is measured along a scale, in which each point is placed at equal distance from one another. Interval data always appears in the form of numbers or numerical values where the distance between the two points is standardized and equal. 37 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th
- 38. • When in addition to setting up inequalities we can also form differences. • For eg: for following temp reading 58˚, 63˚, 70˚,95˚,126˚. In this we can write as 126˚> 70˚or 58˚ < 95˚ which simply means that 126˚ is warmer than 70˚ or 58˚ is cooler than 95˚. 38 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th
- 39. • Interval scales are powerful measurement as it incorporates the concept of equality of interval. • Mean is the appropriate measure of central tendency , while standard deviation is mostly used as measure of dispersion. 39 Principles and practices of Biostatistics, B. Antonisamy, 10 July 2017, 7th
- 40. Examples are : -temperature (o does not mean no heat at all) :- calendar dates :- IQ scores (o does not mean no intelligence at all) 40
- 41. RATIO SCALE • Ratio scales have an absolute or true zero of measurement. Eg: zero point on scale of centimeter indicates the complete absence of length or height. • Ratio scales represents the actual amount of variables. • Multiplication and divisions can be used with this scale. • Examples : duration, mass, length, energy and electric charge. CC R Kothari, Research Methodology methods and techniques, 3rd 41
- 42. RATIO DATA • Ratio Data is defined as a quantitative data, with an equal and definitive ratio between each data and absolute “zero” being treated as a point of origin. In other words, there can be no negative numerical value in ratio data. • In this sense, ratio data includes all the usual measurement of length, height, money amounts, weight, volume, area, pressures etc. 42 Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition, New Delhi.
- 43. MEASURES OF CENTRAL TENDENCY- AVERAGES • Information from a series of observations is summarized by an observer to get answers • Average value of a characteristic is the one central value around which all other observations are dispersed. • In larger series, nearly 50% observations lie above while 50% remains below the central value. 43 C R Kothari, Research Methodology methods and techniques, 3rd edition, Jaipur
- 44. • Central value helps 1) to find which group of the normal observation lie close to central value, while few others of the too large or too small lie far away at both the ends. • 2) to find which group is better off by comparing the average of one group with that of the other • Average is a general term which describes the center of the series. 1. MEAN 2. MEDIAN 3. MODE 4. STANDARD DEVIATION 44 C R Kothari, Research Methodology methods and techniques, 3rd edition, Jaipur
- 45. MEAN • This measure implies arithmetic average or arithmetic mean which is obtained by summing up all the observations and then dividing the total by the number of observation. it is one central value, most usually used in statistical methods. 45 C R Kothari, Research Methodology methods and techniques, 3rd
- 46. MEDIAN • When all the observations are arranged in either ascending or descending order, the middle observation is known as median. • It implies the mid value of the series. 46 C R Kothari, Research Methodology methods and techniques, 3rd
- 47. • Median, therefore, is a better indicator of central value when one or more of the lowest or the highest observations are wide apart or not so evenly distributed. 47
- 48. MODE • This is the most frequently occurring observation in a series, that is most common or most fashionable. • Mode is rarely used in medical studies. 48 C R Kothari, Research Methodology methods and techniques, 3rd edition, Jaipur
- 49. STANDARD DEVIATION • The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range. 49
- 50. GOODNESS OF MEASUREMENT SCALES • Certain characteristics are: a) Validity: content validity and criterion-related validity b) Relevance: (judged to be proper measure) c) Freedom from bias: (equal opportunity) d) Reliability: (criterion is stable/ reproducible) e) Availability: (information must be available) 50
- 51. CONCLUSION Data type is an important concept of statistics, which should be understood to implement statistical methods or procedures correctly. Proper knowledge of data types is necessary to analyze data sets with appropriate statistical methods. Two types of measures : qualitative and quantitative 4 types of scales : nominal, ordinal, interval and ratio Measurement scales : comparative and non-comparative scales. 51
- 52. 52 QUANTITATIVE DATA QUALITATIVE DATA DISCRETE CONTINOUS NON- NUMERICAL RATIO SCALE NOMINAL SCALE ORDINAL SCALE INTERVAL SCALE
- 53. REFERENCES • Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition, New Delhi. • Principles and practices of Biostatistics, B. Antonisamy, 10 July 2017, 7th edition. • Fava GA, Tomba E, Sonino N ,Clinimetrics: the science of clinical measurements. 53
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