Topic 6 stat basic concepts


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Topic 6 stat basic concepts

  1. 1. Statistics: Basic Concepts
  2. 2. Overview• Survey objective: – Collect data from a smaller part of a larger group to learn something about the larger group.• What is data ? How de we describe them? – Observations (such as measurements, genders, survey responses) collected. Statistical Inference 2
  3. 3. Statistics• Statistics: Science which describes or make inferences about the universe from sample information.• Descriptive Statistics: Refers to numerical and graphic procedures to summarize a collection of data in a clear and understandable way.• Inferential Statistics: Refers to procedures to draw inferences about a population from a sample.• In sum, Statistics refers to a set of methods to plan experiments, obtain data, and then organize, summarize, present, analyze, interpret, and draw conclusions based on the data. Statistical Inference 3
  4. 4. Definitions• Population: The set of all elements (scores, people, measurements, and so on) for study .• Census: Collection of data from every member of the population.• Sample: a sub-collection of members drawn from a population. Statistical Inference 4
  5. 5. Key Concepts• Sample data must be collected in a scientific manner, say, through a process of random selection.• If not, collected information will be useless & statistical gymnastic would not salvage. Statistical Inference 5
  6. 6. Types of Data• Parameter: A numerical measurement to describe some characteristic of a population.• Statistic: A numerical to describe some characteristic of a sample. Statistical Inference 6
  7. 7. Definitions• Quantitative data: Numbers representing counts or measurements.• Qualitative (categorical/attribute) data: Data specified by some non-numeric characteristics (for example, gender of participants). Statistical Inference 7
  8. 8. Quantitative DataDiscrete: When the number of possible values is finite or countable number of possible values – 0,1,2,3,…Example: Number of cars parked outside the campus.• Continuous: Infinite number of values pertaining to some continuous scale without gaps.• Example: Milk yield of a cow. Statistical Inference 8
  9. 9. Levels of Measurement• Nominal: Data on names, labels, or categories that cannot be ordered.• Example: Survey responses: Yes, No, Undecided.• Ordinal: Data that can be ordered but their difference cannot be determined or are meaningless.• Example: Course grades A, B, C, D, or F Statistical Inference 9
  10. 10. Levels of Measurement• Interval: Ordinal with the additional property that difference between any two values is meaningful but here is no natural starting point (none of the quantity is present).• Example: Years: 1900, 1910,… Statistical Inference 10
  11. 11. Levels of Measurement• Ratio: Modified interval level to include the natural zero starting point- differences and ratios are defined.• Example: Prices of chocolates. Statistical Inference 11
  12. 12. Levels of Measurement• Nominal - categories only• Ordinal - categories with some order• Interval - differences but no natural starting point• Ratio - differences and a natural starting point Statistical Inference 12
  13. 13. Methods of sampling• Random Sampling: Members of a population selected in such a way that every member has equal chance of getting selected.• Simple Random Sample: Sample units selected in such a way that every possible sample of the same size n has the same chance of selection.• Systematic Sampling: Select some staring point and then select every k-th member in the population Statistical Inference 13
  14. 14. Methods of sampling• Convenience Sampling: Use results easy to obtain.• Stratified Sampling: Subdivide the population into at least two different groups with similar characteristics and draw a sample from each group.• Cluster Sampling: Divide the population into clusters , randomly select clusters, choose all members of the chosen clusters. Statistical Inference 14
  15. 15. Relevant Definitions• Sampling error: Difference between a sample estimate and the true population estimate – error due to sample fluctuations.• Non-sampling error: Errors due to mistakes in collection, recording, or analysis (biased sample, defective instrument, mistakes in copying data). Statistical Inference 15
  16. 16. Relevant Definitions• Reliability: An estimate is reliable when there is consistency on repeated experiments.• Validity: An estimate is valid when it has measured what it is supposed to measure. Statistical Inference 16