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# Statistics, Week 1 PSTL1004

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This 7 page Class Notes was uploaded by Jonathan Femi-Cole on Saturday February 13, 2016. The Class Notes belongs to PSTL1004 at a university taught by Suzanne Loch in Winter 2016. Since its upload, it has received 33 views.

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Date Created: 02/13/16

Introduction • There are statistics about crime, sports, education, politics, and real estate. • Statistical methods can help you make the "best educated guess." • The fields of economics, business, psychology, education, biology, law, computer science, police science, and early childhood development require at least one course in statistics. • statistics and probability work together. • you will learn how to organize and summarize data. • Organizing and summarizing data is called descriptive statistics. • Two ways to summarize data ○ Graphing ○ Numbers • inferential statistics: uses probability to determine how confident we can be that the conclusions are correct. • Inference: Effective interpretation of data ○ based on good procedures for producing data and thoughtful examination of the data. • The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life. Statistics • level of measurement: The way a set of data is measured • Not every statistical operation can be used with every set of data. • Classified into four levels of measurement (lowest to Highest) ○ Nominal Scale Level ○ Ordinal Scale Level ○ Interval Scale Level ○ Ratio Scale Level • nominal scale: Data measured is qualitative. ○ Categories, colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data. • Ordinal Scale: Data can be measured ○ An example of ordinal scale data is a list of the top five national parks in the United States. The top five national parks in the United States can be ranked from one to five but we cannot measure differences between the data. • interval scale: Can be measured ○ Temperature scales like Celsius (C) and Fahrenheit (F) are measured by using the interval scale. • Ratio Scale: Can Be measured ○ For example, four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points). • Qualitative: (hair color, ethnic groups and other attributes of the population) • Quantitative: (distance traveled to college, number of children in a family, etc.) ○ Discrete: Data is discrete if it is the result of counting (the number of students of a given ethnic group in a class, the number of books on a shelf, etc.). ○ Continuous: Data is continuous if it is the result of measuring (distance traveled, weight of luggage, etc.) Probability: • Probability is a mathematical tool used to study randomness. • The theory of probability began with the study of games of chance such as poker. • In your study of statistics, you will use the power of mathematics through probability calculations to analyze and interpret your data. Key Terms: • Population: an entire collection of persons, things, or objects under study. • Sampling: to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. • sampling methodology: Way data is collected with the sample. (Paper handouts, interviews, etc) • Data: The result of sampling and population • Statistic: is a number that is a property of the sample. • Parameter: a number that is a property of the population. • Representative Sample: Must contain the characteristics of the population • Variable: notated by capital letters like X and Y, is a characteristic of interest for each person or thing in a population. ○ Numerical variables: take on values with equal units such as weight in pounds and time in hours ○ Categorical variables: place the person or thing into a category. • X (calculate the average number of points earned, for example) • Y (calculating an average party affiliation makes no sense). • Data: The actual values of the Variable • Datum: A single Value • Proportion: A proportion is the number of successes divided by the total number in the sample. Data • Qualitative Data: the result of categorizing or describing attributes of a population. Hair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. ○ quantitative data over qualitative data because it lends itself more easily to mathematical analysis. For example, it does not make sense to find an average hair color or blood type. • Quantitative Data: Quantitative data are the result of counting or measuring attributes of a population. Amount of money, pulse rate, weight, number of people living in your town, and the number of students who take statistics are examples of quantitative data. ○ Discrete: takes on a certain number of numerical values, increases 1, 2, 3, etc ○ Continuous: contains a measurement of continuous data The 5W's • The 5 W’s are questions we ask in order to understand our data • who, what, why, where, when, and how. • ‘who’ question tell us the cases or who the data is coming from. • When we collect data from a survey we call these cases respondents. • experimental units: collecting data from an inanimate object • ‘what’ question of the 5 W’s refers to the variables or the questions you have for the respondents. • ‘why’ question is the purpose of the study, the reason you are asking questions of the cases. This is your guiding research question. • ‘When’ is the date and time of the data collection process. Example: Pew Charitable Trusts conducted a longitudinal study that has followed families from 1968 to the present to gain a better understanding of the American Dream and economic mobility. They surveyed 2227 American families asking, “What is your “Family income” including all taxable income (such as earnings, interest, and dividends) and cash transfers (such as Social Security and welfare) of all family members?” Identify the 5W’s of this example. Who: 2227 American families What: Family income Why: To understand the relationship between the American Dream and economic mobility. Where: United States of America When: 1968 to present How: Longitudinal study Sampling • A sample should have the same characteristics as the population it is representing. • Random Sampling ○ each member of a population initially has an equal chance of being selected for the sample. • Simple Random Sample (population needs to be countable and each member identified) ○ Any group of n individuals is equally as likely to be chosen as any other group of n individuals if the simple random sampling technique is used. • Multistage sample ○ Pick a day, random number within that day ○ Multiple layers • Stratified Sample ○ divide the population into groups called strata and then take a proportionate number from each stratum. • Cluster Sample ○ cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. • Systematic Sample ○ systematic sample, randomly select a starting point and take every certain number (2nd, 3rd, 4th, etc) piece of data from a listing of the population. • Convenience Sampling: nonrandom and involves using results that are readily available (ex. Friends, not a good sample) • Replacement: Form of true random sampling. once a member is picked that member goes back into the population and thus may be chosen more than once. • Without Replacement: Once a member is picked from the population, they cannot re-enter the population. • Sampling Bias: created when a sample is collected from a population and some members of the population are not as likely to be chosen as others (remember, each member of the population should have an equally likely chance of being chosen) Can result in incorrect conclusions drawn about the population Variation and Critical Evaluation • Variation is present in any set of data. ○ For example, 16-ounce cans of beverage may contain more or less than 16 ounces of liquid. Variation In Samples • two or more samples from the same population • taken randomly • having close to the same characteristics of the population • are different from each other. Size of Sample • often called the number of observations • Many large samples are biased. • Sample: A portion of the population understudy. A sample is representative if it characterizes the population being studied. • Population: The collection, or set, of all individuals, objects, or measurements whose properties are being studied. Sampling and Data: Answers and Rounding Off • Rounding off ○ carry your final answer one more decimal place than was present in the original data ○ Round only the final answer. Sampling and Data: Frequency, Relative Frequency, and Cumulative Frequency • Frequency: the number of times a given datum occurs in a data set. • Relative Frequency: the fraction or proportion of times an answer occurs ○ divide each frequency by the total number of things in the sample • Cumulative Relative Frequency: the accumulation of the previous relative frequencies. ○ add all the previous relative frequencies to the relative frequency for the current row. Sampling and Data: Summary • Average A number that describes the central tendency of the data. There are a number of specialized averages, including the arithmetic mean, weighted mean, median, mode, and geometric mean. • Continuous Random Variable A random variable (RV) whose outcomes are measured. Example: The height of trees in the forest is a continuous RV • Cumulative Relative Frequency (cum. rel. freq. or cum RF) An accumulation of the previous relative frequencies. The Cumulative Relative Frequency is the sum of the relative frequencies for all values that are less than or equal to the given value. • Data A set of observations ○ qualitative (hair color, ethnic groups and other attributes of the population) ○ quantitative (distance traveled to college, number of children in a family, etc.) § Discrete: if it is the result of counting (the number of students of a given ethnic group in a class, the number of books on a shelf, etc.) § Continuous: if it is the result of measuring (distance traveled, weight of luggage, etc.) • Discrete Random Variable: A random variable (RV) whose outcomes are counted. • Frequency (freq. or f) • The number of times an answer occurs • Population The collection, or set, of all individuals, objects, or measurements whose properties are being studied. • Probability Mathematical tool used to study randomness. A number between 0 and 1, inclusive, that gives the likelihood that a specific event will occur. • The 5 W's Who What Where When Why How

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