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Statistics-MAT 150 Chapter 1 Introduction to Statistics. Prof. Felix Apfaltrer fapfaltrer@bmcc.cuny.edu Office:N518 Phone: x7421. Chapter 1. Overview Nature of data Skills needed in statistics. Statistics: Descriptive Analyze nature of data from surveys, experiments, observations,

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statistics mat 150 chapter 1 introduction to statistics

Statistics-MAT 150Chapter 1Introduction to Statistics

Prof. Felix Apfaltrer

fapfaltrer@bmcc.cuny.edu

Office:N518

Phone: x7421

chapter 1
Chapter 1
  • Overview
  • Nature of data
  • Skills needed in statistics
overview
Statistics:

Descriptive

Analyze nature of data from surveys, experiments, observations,

Inferential

Draw conclusions from the analyses with respect to the population

Survey: tool to collect data from a smaller group which is part of a larger group to learn something about the larger group

Overview
  • Key goal of statistics:
  • Learn about a large group
  • (population) from data from
  • from a smaller subgroup
  • (sample)
overview1
Definitions:

Data: observations collected (measurements, gender, answers,…)

Statistics: collection of methods to analyze data

Population: complete collection of elements (scores, measurements, subjects,…)

Sample: subcollection of members from selected population

Census: collection of data from every member of the population

Overview
overview 2
Overview 2

Example:

  • Poll: 1087 adults are asked whether they drink alcoholic beverages or not.
    • Sample: 1087 adults
    • Population: US adults 150 million.
  • Census: Every 10 years, the census bureau tries to collect information from every member of the US population.
    • Impossible!
    • Very expensive!
  • Use sample data to draw conclusions from whole population: inferential statistics!
types of data
Types of data

Parameter:

  • A numerical measurement describing some characteristic of the population.
  • Lincoln elected: 39.82% of 1,865,908 votes counted.
    • 39.82% is a parameter.

Statistic:

  • A numerical measurement describing some characteristic of the sample.
  • Based on a sample of 877 elected executives, 45% would not hire an applicant with a typographical error in the application.
    • 45% is a statistic.
types of data 2
Types of data 2

Quantitative data:Numbers representing counts or measurements.

  • Weights of supermodels.

Qualitative data: Nonnumerical.

  • Gender of an athlete.

Discrete vs. continuous data

  • # of people in a household vs. temperatures in May.

Nominal level of measurement: names, labels categories: no ordering.

  • Yes/No/Undecided responses, colors.

Ordinal level of measurement: some order, but numerical values meaningless or nonexistent.

  • Course grades A, B, C, D, F. “Livability rank of a city”.

Interval level of measurement: order, but “no 0” or meaningless.

  • Temperature, year.

Ratio level of measurement: as before with meaningfull zero.

  • Weights, prices (non-negative).
basic skills
Basic skills

Samples:

  • representative:
  • “39/40 polled people vote for A” Sampled in A’s headquarters!
  • Not too small:
  • CDF published “among HS students suspended, 67% suspended more than 3 times” Sample size: 3!

Graphs: In which one does red do better?

Percentage of:

  • 6 % of 1200 = 6 / 100 * 1200 = 72%

Fraction >>> percentage:

  • 3/4 = 0.75 >>> 0.75 * 100% = 75 %

Percentage >>> decimal:

  • 27.3% = 27.3/100 = 0.273

Decimal >>> percentage:

  • 0.852 >>> 0.852 * 100%

= 85.2%

  • `
basic skills 2
Basic skills 2

Calculator:

design
Design

Observational study: observe and measure characteristics without trying to modify subjects.

  • Gallup poll.
  • Cross-sectional: data observed, measured at one point in time.
  • Retrospective: data are collected from the past (records)
  • Prospective: data collected along the way from groups (smokers/NS)

Experiment: apply treatment and observe and measure effects.

  • Clinical trial for Lipitor.
  • Control: blinding - placebo, double-blinding, blocks
  • Replication: ability to repeat experiment
  • Randomization: data needs to be collected in an appropriate (random) way, otherwise it is completely useless!
    • Random sample: members of the population are selected so that each individual member has the same chance of being selected.
    • Simple random sample of size n : every possible random sample of size n has the same chance of being chosen.
design 2
Design 2

Sampling:

  • systematic: select starting point and every kth member chosen.
  • convenience: use easy to get data
  • stratified: subdivide population into at least 2 subgroups with common characteristic and draw samples from each (e.g. gender or age)
  • cluster: divide population into areas and draw samples form clusters

Sampling error: the difference between a sample result and the true population result; results from chance sample fluctuations

Nonsampling error: occurs when data is incorrectly collected, measured, recorded or analyzed.