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# Intro To Social Statistics SOC 3400

UH

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This 4 page Class Notes was uploaded by Marco Ferry on Saturday September 19, 2015. The Class Notes belongs to SOC 3400 at University of Houston taught by Staff in Fall. Since its upload, it has received 55 views. For similar materials see /class/208362/soc-3400-university-of-houston in Sociology at University of Houston.

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Date Created: 09/19/15

SOCIOLOGY 3400 INTRODUCTION TO SOCIAL STATISTICS Summer 2012 REVIEW TOPICS 7 EXAM 1 What are the four levels of measurement NOIR 7 Nominal Ordinal Interval and Ratio level of measurement Nominal measurement numbers or other symbols are assigned to a set of categories for the purpose of naming labeling or classifying the observations Ordinal measurement numbers are assigned to rankordered categories ranging from low to high Interval level measurement 7 numbers indicate more or less of some phenomenon and the differences between numbers are the same There are meaningful distances Ratio level measurement quantitative variables which have all the properties of interval variables and a meaningful 0 point The value of 0 indicates the lack of phenomenon How do nominal variables differ from ordinal measures Nominal variables are often qualitative they vary in quality inherent in each rather than quantity EX political party religion race How do ordinal variables differ from interval measures Ordinal variables have numbers that indicate more or less of some phenomenon but numbers do not express the degree of difference EX Social class 4 upper class 3 upper middle class 2 lower middle class 1 working class How do interval variables differ from ratio measures Interval variables have no meaningful 0 value and ratio level measure do Both types of variables display a specific magnitude of difference shows how much larger or smaller the difference Ratio level measurement includes all of interval characteristics plus a meaningful 0 value EX Interval variables 7 IQ scales psychological scales temperature EX Ratio variables Income number of crimes number of hours How does a proportion differ from a percentage A proportion is a relative frequency obtained by dividing the frequency in each category by the total number of cases p fN It is the quotient of one group over the total number of observations and can indicate the probability of an event A percentage is a relative frequency obtained by dividing the frequency in each category by the total number of cases and multiplying by 100 proportion X 100 What types of graphs are appropriate to summarize qualitative or nominal data Pie chart Bar graph What types of graphs are best suited to summarize quantitative data Bar graph Histogram Line graph What measures of central tendency are most appropriate to summarize nominal ordinal interval and ratio level data Mode 7 appropriate to summarize NOIR7 nominal ordinal interval ratio level data Median 7 appropriate to summarize OIR 7 ordinal interval and ratio level data Mean 7 appropriate to summarize IR 7 interval and ratio level data Know how to calculate a proportion in your head p f proportion frequency in each category divided by the total number of cases N Know how to calculate the mode median and mean using your book Know how to interpret the value of the mode median and mean Mode the category or score with the highest frequency or percentage in the distribution Locate most common category Median 7the score that divides the distribution into two equal parts so that half the cases are above it and half below it First order the responses from low to high if odd number of cases choose middle value or category If even number or cases nd the two middle cases and divide by 2 Mean a measure of central tendency that is obtained by adding up all the scores and dividing by the total number of scores It is the arithmetic average Add up all responses divide by the total number of responses Y N How can you tell if data might be skewed by examining the mode median and mean What should the values of the mode median and mean be if the data have positive skew What should the values of the mode median and mean be if the data have negative skew Skewed distributions have a few extreme values on one side of the distribution Positive Skew 7 Mode lt Median lt Mean the mean is pulled in the direction ofthe positive scores distribution with a few extremely high values Negative Skew 7 Meanlt Median lt Mode the mean is pulled in the direction of the lower scores distribution with a few extremely low values What does the value of a standard deviation tell you about the distribution of data Standard deviation is a measure of variation for interval ratio variables it is equal to the square root of the variance or equal to the square root of the average of the squared deviations from the mean A larger standard deviation indicates wider dispersion of points below or above the mean It tells how far on average data points are from the center of distribution mean Memorize the approximation formula for the standard deviation presented in class Be able to calculate an approximation for the standard deviation from memory Standard deviation approximation can be used if the data is symmetrical and mound shaped presents a normal distribution Sy Range highest value 7 lowest value 4 4 Be able to calculate a variance using the computational formula presented in class You do not need to memorize this formula but be able to use the formula S2y ZgYYV Variance the sum of the squared deviations from the mean divided by the number of Nl scores minus 1 If you were given the value of a variance how would you calculate the standard deviation in your head The standard deviation is equal to the square root of the variance average of the squared deviations from the mean Sy Szy or Sy V21 Y E g2 N l hm Pctx cnmgn L ndcnlv Normal me Regarding the standard deviation and the mean within what range of values should you nd about 68 of all data points 39 95 of all data points 99 of all data points Assume the Mquot data are symmetrical and moundshaped 5 v 68 of all data points fall within 1 standard deviation of the mean m 95 of all data points fall within 2 standard deviation of the mean L 1 m muggimggwiag 99 of all data points fall within 3 standard deviation of the mean How does a statistic differ from a parameter That is what does a statistic tell you What does a parameter tell you A statistic is a measure mean or standard deviation used to describe a sample distribution EX sample mean sample proportion and sample standard deviation A parameter is a measure mean or standard deviation used to describe a population distribution EX population mean population proportion population standard deviation Know how to calculate a Z score from memory Z Y YZ score Raw score mean Sy standard deviation How do you interpret the value of a Z score A standard Z score is the number of standard deviations that a given raw score is above or below the mean It represents how far a given raw score is from the mean in standard deviation units Positive Z score a score is larger than the mean Negative Z score a score is smaller than the mean The larger the Z score the larger the difference between the score and the mean What is a standard normal distribution What is the value of the mean and standard deviation of a standard normal distribution A standard normal distribution is a normal distribution represented in standard Z score with Mean 0 and Standard Deviation 1 Areas or proportions under the standard normal curve correspond to any Z score or its fraction organized in the standard normal table What is a sampling distribution of means Sampling distribution of the mean is the theoretical probability distribution of sample means that would be obtained by drawing from the population all possible samples of the same size If we repeatedly drew samples from a population and calculated the sample means those sample means would be normally distributed as samples drawn increases What is the standard deviation of a sampling distribution of means called Standard Error of the Mean How do you interpret the value of the standard deviation derived from a sampling distribution of means It describes how much dispersion there is in the sampling distribution of the mean or how much variability there is in the value of the mean from sample to sample According to the Central Limit Theorem what is the speci c numerical value of the average of a distribution of sample means According to the Central Limit Theorem what is the speci c numerical value of the standard deviation of a distribution of sample means Approximately how large should a sample size be in order for the Central Limit Theorem to be applicable Within what range of values should you nd approximately 95 of all sample means from the true population mean What is a sampling distribution of proportions What is the standard deviation of a sampling distribution of proportions called Standard Error of the proportion How do you interpret the value of the standard deviation derived from a sampling distribution of proportions Know how to calculate a 95 con dence interval for a mean from a given formula How do you interpret the value of a 95 con dence interval for a mean 95 CI Yi Z 639 9 95 CI Yi S3 63 g 337 21 N v We are 95 con dent that the true population mean is somewhere between the calculated upper and lower boundaries Know how to calculate a 95 con dence interval for a proportion from a given formula How do you interpret the value of a 95 con dence interval for a proportion 95 CI pi Z Sp Sp leLnll N We are 95 con dent that the true population proportion is somewhere between the calculated upper and lower boundaries

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