Statistics: Basic Concepts

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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.

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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.

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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.

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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.

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Types of Data

• Parameter: A numerical measurement to describe some characteristic of a population.

• Statistic: A numerical to describe some characteristic of a sample.

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Definitions

• Quantitative data: Numbers representing counts or measurements.

• Qualitative (categorical/attribute) data: Data specified by some non-numeric characteristics (for example, gender of participants).

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Quantitative Data

Discrete: 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.

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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

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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,…

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Levels of Measurement

• Ratio: Modified interval level to include the natural zero starting point- differences and ratios are defined.

• Example: Prices of chocolates.

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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

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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

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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.

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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).

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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.