Statistics 401, Week 2
Statistics 401, Week 2 01:960:401
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This 2 page Class Notes was uploaded by Wendy Liu on Friday September 16, 2016. The Class Notes belongs to 01:960:401 at Rutgers University taught by Hei-ki Dong in Fall 2016. Since its upload, it has received 281 views. For similar materials see Basic Statistics for Research in Statistics at Rutgers University.
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Date Created: 09/16/16
Chapter 1 & 2: Intro to Stat, Organization & Description of Data 13 September 2016 Basic Stat for Research Professor HK Dong Wendy Liu Statistics – collecting, summarizing, interpreting data and then drawing conclusions Objectives of Statistics 1. Make inferences about a population by analyzing info from a sample a. Includes assessing the extent of uncertainty involved in these inferences 2. Design the process and extent of sampling so that the sample is representative of the population, and thus inferences are valid Inferential statistics – evaluate info present in data, assess the new learning gained from this info Descriptive statistics – summarize and describe prominent features of data: 3 S’s Shape o Normal – symmetric, bell shape curve o Skewness o Uniform o Bimodal Spread (variation) o Range – difference btwn largest and smallest observations o Interquartile range (IQR) – middle 50% of data IQR = Q3-Q1 o Standard deviation o Variance Central tendency o Mean – average of set o Median – Q 2 middle value of ordered measurements Positioning point: = value corresponding to median Points ending in (x.5) occurs for even data sets (sets with even n) Take average of data values corresponding to x.5±0.5 o Mode – most frequent data meaurement Unit/subject – single entity from which you collect data Ex: person Population of units/subjects – complete collection of units from which you collect data Ex: American citizens Population – large set of all potential measurements corresponding to the population of units Ex: age of all American citizens Sample – subset of measurements that are actually collected during investigation Ex: age of 40 American citizens Statement of purpose – the reason to collect data; must be specific and unambiguous Types of Data 1. Qualitative – classified in categories, not numerically measured 2. Quantitative/numerical/measurement – variables measured w/ numbers Discrete – gaps btwn neighboring distinct values Continuous – no gaps btwn neighboring values Organizing quantitative data Ordered array: list all data smallest to largest/largest to smallest Visual representations: o Frequency distributions + cumulative distributions Histogram – like a bar graph, but for quantitative data (number line on x-axis) Polygon Ogive – like a polygon, but cumulative o Stem + leaf plot For smaller sets of data o Dot plot – dots on top of a number line representing each data point Frequency distributions for continuous variables Class intervals – cover ranges of equal length w/o overlapping Class boundaries – endpoints of intervals Class frequency – number of observations belonging to each class interval Relative frequency – percentage of observations in each class out of total observations Common Notations ∑ Summation – addition of set of values x Variable representing individual data values n # of values in sample N # of values in population x bar – mean of all x values