Week 1 and 2: Intro Statistics in Social Science
Week 1 and 2: Intro Statistics in Social Science 1053
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This 5 page Bundle was uploaded by Alexis Mebane on Friday September 19, 2014. The Bundle belongs to 1053 at George Washington University taught by Dr. Srinivasan Balaji in Fall2014. Since its upload, it has received 80 views. For similar materials see Intro-Statistics in Social Science in Statistics at George Washington University.
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Date Created: 09/19/14
Week 1 and 2 Statistics 1053 IntroStats in Social Science Week 1 What is Statistics The science of collecting classifying summarizing organizing analyzing and interpreting data 0 Two types of Statistics 0 Descriptive Statistics classifying summarizing and organizing data I Numerical and graphical methods are used to look at patterns in the data set no analysis 0 Inferential Statistics analyzing and interpreting data I Samples are used to make estimates decisions and predictions about the population I Probability theory is a key tool for analysis 0 Applications of Statistics 0 Estimate the average monthly income for a population 0 Determine effectiveness of a certain drugvaccine o Pre election opinion polls to predict a winner Fundamental Elements and Definitions Population a collection of individuals objects under study I Samplesubset of the population Variable a characteristic of interest about each individual element of the populationsample I Types of Variables Qualitative categorical and Quantities numerical o Qualitative non numerical variables I Examples blood types letter grades zip codes of home addresses for students I Qualitative date can be summarized in 2 ways Tabular Frequency Distributions and Graphical Box plot and Bar chart o Quantities variables with numerical values I Examples wait time at the Foggy Bottom metro number of freshman enrolled from 3990 to 3910 Data Collection can be obtained in various ways Sampling should represent the population should have characteristics that represent the total population Simple Random Sampling SRS 0 Each element in the population has an equal chance of being chosen This sample is obtained by samples with replace OR samples without replacement Systematic o The first in random and then every nth element is picked Elements need to be in to be sorted and ordered 0 Stratified Random Sampling 0 Obtained by first stratifying sample and then selecting a fixed number of elements by SRS Cluster 0 Obtained by sampling some but not all of the possible subdivisions of population Frequency Distribution 0 Tabular summary showing the different classes and the frequency the number of items in each of the several and nonoverlapping classes 0 Shows how observations are distributed Objective to provide insight about the data that cannot be quickly obtained by looking at the original o Example 1 Letter Grades Frequency Relative Frequency A 3 3 B 4 4 C 2 2 D 1 1 Relative Frequency Relative frequency should be equal to 1 frequency total of values 0 Example 2 Rati ue Relative F Poor 1 Below A 1 Average 25 Good 45 Exce ent 1 Bar Chart I Horizontal Axis Levels of Qualitative Variables I Vertical Axis Frequency Relative Frequency Pie Chart 0 A class with a relative frequency of 25 would consume 90 degrees of the chart 0 Multiply the relative frequency by 360 to determine what the angle of each variable should be Quantities Data measurements that can be measured on numerical scale I Graphical Methods 0 StemLeaf 0 Frequency Relative Frequency Distribution 0 Histogram 0 Dot Plot StemLeaf I Every observation gets divided into 2 I Leaf right most digits I Stem the remaining values Fre uenc Relative Fre uenc Distribution I Put data into a table I Range is partitioned into a number of classes of equal width I Frequency Distribution table is constructed by counting the frequency of observations in each class I Guidelines use between 520 classes the larger the dataset the more classes use classes of equal width draw them adjacent to each other class width is greater than or equal to largest observation smallest observation of classes I Distribution could be skewed or symmetric If skewed follow the tail If the tail is on the left side then it39s left or negatively skewed and vice versa 0 Summation Notation 0 Summation Notation is fairly simple and it is marked by the symbol Ex I Ex is the way to show X1X2Xn I Examples 39 2x37451130 XXV 30 900 X2 32 7242 52 112 220 I 2x1 2 6 3 4 10 25 OR Ex n n sample size Week 2 Numerical Summarythe want to summarize the dating using numerical descriptive measures 0 2 quantities center the measure of the central tendency variability the spread of data Mean the average of a group of numbers this is not applicable for qualitative data only quantitative affected by all numbers in the data set Median the middle most observation the middle value not affected by extreme values or outliers Mode the most frequent observation 0 NOTE I Negatively skewed distributions meanltmedianlt mode 0 Positively skewed distributions medianltmeanltmode I Symmetric distributions mean median mode 0 Measures of Spread 0 Range Maximum minimum o Variance the squared distance between typical observations and the mean of the data 39 02 ZXu2 N Sample variance S22nx1 X2I11 0 Standard Deviation the average distance between an observation and the mean Population 6Z X11n1 Sample S Zx mean 2 n 1 The Empirical Rule sometimes the distribution is symmetric bell shaped when this happens the mean the standard deviation together can describe the distribution fairly well Most observations lie in near the center 0 XiS is 68 of the data 0 Xi2S is approximately 95 of the data 0 Xi3S is approximately 997 of the data Chebyshev s Rule for any dataset the following are true 1 at least 75 of the data falls between the meani2s 2 at least 89 of the data falls between meani3s 3 at least 94 of the data falls between the meani4s Of standard Distance from the Min proportion of the deviations mean value K 2 uJr26 1122 75 K3 ui36 1132 89 K4 p4a 1142 94
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