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# Lecture 1

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Numaracy for the Business Environment

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### Lecture 1

1. 1. 1
2. 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. 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. 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. 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. 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. 7. • Basic concepts of Statistics – Census • Investigate the whole population • Expensive • Time consuming • Sections of population is inaccessible • Units are destroyed • Inaccurate 7
8. 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. 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. 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. 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. 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. 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. 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. 15. DIFFERENT TYPES OF DATA QUANTITATIVE QUALITATIVE (numerical scale) (categorical)Discrete Continuous(integer) (any numerical value) 15
16. 16. DIFFERENT TYPES OF DATA QUANTITATIVE QUALITATIVE(numerical scale) (categorical) Nominal Ordinal Interval Ratio scaled scaled scaled scaled 16
17. 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. 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. 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. 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. 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. 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