Lecture 1
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- 2. • Statistics is the science of data collection, organising and interpreting numerical facts. • Gaining information from numerical data or making sense of data. • Descriptive Statistics – Organising and summarising data – condense large volumes of data into a few summary measures. • Statistical inference – Generalises subset data findings to the broader universe. 2
- 3. • Statistical analysis in management decision-making Input Process Output → Statistical Decision → Data → → Information → Analysis Making → Useful, Raw Transformation Usable Observations Process Meaningful MANAGEMENT DECISION SUPPORT SYSTEM 3
- 4. • Approach for the Statistical process Research process becoming a cycle PLANNING DECISION- DATA MAKING COLLECTION Primary and Descriptive Statistics secondary Statistical inference sources EDITING CONCLUSIONS and CODING ANALYSIS 4
- 5. • Basic concepts of Statistics – Parameter • Computed from the universe. – Statistic • Computed from the subset taken from the universe. – Variable • Characteristic of the item being observed or measured. – Data • Collection of observations on one or more variable. 5
- 6. • Basic concepts of Statistics – Population • Entire group we want information about. – Sample • The proportion of the population we actually examine. • Representative and not biased. • Random sampling. 6
- 7. • Basic concepts of Statistics – Census • Investigate the whole population • Expensive • Time consuming • Sections of population is inaccessible • Units are destroyed • Inaccurate 7
- 8. • Sampling methods – Probability sampling • Each element has a known probability of being selected as part of sample. • Unbiased inference about the population. – Non-probability sampling • Element from the population are not selected random. • The elements are selected without knowing the probability of being selected as part of sample. • We can not use results of these samples to make conclusions about the population. 8
- 9. • Sampling methods – Probability sampling – Simple random sampling • Number the elements of the population from 1 to N. • Select a random starting point in the random table. • From the starting point read systematically in any direction. • Divide the digits in the random table into groups with the same number of digits as the number of digits in the population size (N). • Find n random numbers from 1 to N – no duplicates. • Identify each of the chosen random numbers in the population. 9
- 10. • Sampling methods – Probability sampling – Stratified random sampling • Population heterogeneous with respect to the variable under study. • Population divided into N = N1 + N2 + ….. + Nk homogeneous sub- populations called strata. (k = number of stratum) • Sample size form each n = n1 + n2 + ….. + nk sample proportional to (k = number of stratum) stratum size. • Draw a simple random sample N from each of the stratum. n i n, i 1...k i N 10
- 11. • Sampling methods – Non-probability sampling – Convenience sampling • Not representative of the target population. • Items being selected because they are easy to find, inexpensive and self selected. 11
- 12. • Sampling methods – Non-probability sampling – Quota sampling • Population divided into sub-classes according to a certain characteristic. • A non-sampling method is used to select a sample from each stratum. • It is a technique of convenience. • Researcher attempts to fill the quota quickly. • Sample is not representative of the population. 12
- 13. • Sampling methods – Non-probability sampling – Judgement sampling • Elements from the population are chosen by the judgement of the researcher. • The probability that an element will be chosen cannot be calculated. • Sample is biased. 13
- 14. • Sampling methods – Non-probability sampling – Snowball sampling • Is used where sampling units are difficult to locate and identify. • Find a person who fits the profile of characteristics of the study. • From this person obtain names and locations of others who will fit the profile. 14
- 15. DIFFERENT TYPES OF DATA QUANTITATIVE QUALITATIVE (numerical scale) (categorical) Discrete Continuous (integer) (any numerical value) 15
- 16. DIFFERENT TYPES OF DATA QUANTITATIVE QUALITATIVE (numerical scale) (categorical) Nominal Ordinal Interval Ratio scaled scaled scaled scaled 16
- 17. • Problems associated with the collection of data: – Characteristics have to be measured. – Measurements can be complicated. – Measurements must be valid and accurate. – Secondary data not easy to validate. – Data can be incomplete, typographical errors, small sample. – Biased or misleading responses. 17
- 18. • Problems associated with the collection of data: – Make sure of the following: • Who conducted the study? • What data was collected? • What sampling method was used? • Sample size? • Chance of bias? • Is data relevant to the problem at hand? 18
- 19. • How to design a questionnaire – Questions should: • Be simply stated. • Have no suggestion of a specific answer. • Be specific and address only one issue. • Carefully word sensitive issues. • Not require calculations or a study to be answered. – Types of questions: • Closed • Open • Combined 19
- 20. • Appearance and layout of a questionnaire – Attractive look. – Coloured paper. – Clear instructions on how to complete. – Reasonably short. – Enough space to complete questions. – Mother-tongue language. – Interesting questions first. – Simple questions first, controversial questions later. – Complete one topic before starting the next. – Important information first. 20
- 21. • Interview – Fieldworker completed questionnaire • Higher response rate and data collection is immediate. – Mailed questionnaires • When population is large or dispersed. • Low response rate. • Time consuming. – Telephone interview • Lower costs. • Quicker contact with geographically dispersed respondents. 21
- 22. • Editing the data – Obvious errors should be eliminated. – Eliminate questionnaires that are incomplete and unreliable. – Questionnaires should be pre-tested on a small group of people. 22