html5-img
1 / 11

Statistics-MAT 150 Chapter 1 Introduction to Statistics

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,

hadassah-floyd
Télécharger la présentation

Statistics-MAT 150 Chapter 1 Introduction to Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Statistics-MAT 150Chapter 1Introduction to Statistics Prof. Felix Apfaltrer fapfaltrer@bmcc.cuny.edu Office:N518 Phone: x7421

  2. Chapter 1 • Overview • Nature of data • Skills needed in statistics

  3. 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)

  4. 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

  5. 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!

  6. 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.

  7. 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).

  8. 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% • `

  9. Basic skills 2 Calculator:

  10. 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.

  11. 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.

More Related