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Chapter 1-4

by: Amanda Jimenez

Chapter 1-4 PY 211

Amanda Jimenez
GPA 3.3

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Elem Statistical Methods
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This 5 page Class Notes was uploaded by Amanda Jimenez on Sunday March 6, 2016. The Class Notes belongs to PY 211 at University of Alabama - Tuscaloosa taught by a professor in Fall 2015. Since its upload, it has received 13 views. For similar materials see Elem Statistical Methods in Psychlogy at University of Alabama - Tuscaloosa.


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Date Created: 03/06/16
Chapter 1: What is Statistics? Statistics­ science of learning from data and of measuring, controlling and communicating  uncertainty.  Not math: means that things are apparently all over the place.   Statistics is the science of quantifying and understanding variation.  Helps you make sense of info you’re exposed to. Everything varies  Measure the same thing twice you will get different answers. Statistics is all about variation  If the variation you see/observe is larger than the variation you would expect as normal  Statistically significant.  Response variable: variable whose variation you are trying to understand Explanatory Variable: something that takes up different values.  Descriptive statistics: summary of information in a collection of data. Inferential Statistics: provides prediction about a population on the basis of a sample. Population: total set of units of interests. Sample: subset of the population of interest.  Parameter­ # that summarizes a population Statistic: # that summarizes a sample. Random Sampling: idea that each member of a population has equal chance of being selected to  be a part of a sample. Chapter 2 Explanatory Variable: influences variation.  Response Variable: influenced by explanatory variable. Two Methods  Descriptive: summary of information  Inferential: provides predictions about population. Population: total set of units Sample: subset of a population Every number summarized: parameter Use standard deviation  Sample­ when we describe a sample, we are actually defining a statistics of sample.  Parameter estimation: in the absence of all cases from a population, we need to make inferences  about the population parameter based on a sample statistic.  Roles of variables  Response variable: also known as dependent variable (y axis)  Explanatory Variable: independent variable (x axis) Types of variables:  Discrete variables: variables that can only take on specific numbers (#of siblings for ex)  Continuous variable: can take any real number value Categorical variables: categories  Nominal­ 2 or more categories where the order doesn’t matter.  Dichotomous­ only 2 categories  Ordinal­ two or more categories where ORDER MATTERS Quantitative Variable­ characterized by numerical value Interval: numerical values in which intervals between values assumed to be the same Ratio­ meaning the zero point Chapter 3 When you connect data, end up with numbers  Use tables and graphs to summarize data Categorical variables:  Categorical data lists categories and show frequency Frequency distribution:  Listing of all possible values Relative frequency:  Proportion or percentage of the observations that fall in that category Quantitative variables  Frequency distributions are useful for quantitative variables  Need to divide measurement scale in a set of intervals Outliers: extreme observations that fall far from the rest of the data  *observations – troublesome to a lot of statistical procedures,  Cause exaggerated estimates and instability Linear relationship: line that will help you identify the relationship. ­scatter plot Chapter 4 Measures of Tendency  First step in the data analysis=data collection  Once data is collected, you need to organize data  Data entry=important step Data Frame­ object with rows and columns.  Rows contain different observations  Columns contain values of different variables  Values can be quantitative or qualitative Central tendency: everything varies   Shows what the typical observation is  Sample statistic­ also cluster around central values Sample stats: a number that describes all numbers Important math notations:  Notational system­ used to express math operations  Variable represented­ lowercase. Sigma (greek letter that looks like an E) :means sum of everything  Sigma X (greek letter that looks like an E with a x next to it) means sum of all x’s *if there are 30 values we say n=30 Arithmetic Mean: ­Only appropriate for quantitative variables ­most straight forward quantitative measure of central tendency *very important property that is worth knowing about mean is that it is sensitive to outliers* Extremely large or extremely small values will have an effect on mean.  Because the arithmetic mean is sensitive to the outliers, it is usually puled in direction of the  outliers For binary 0­1 data the mean equals proportion of observations that equal 1  Residual­ difference between the number and the mean Mean: only single number of which residuals (distance between each data point and the mean)  sum to 0 Geometric mean For process that change multiplicatively rather than additively, arithmetic mean is not a  good measure Appropriate measure in this case is a geometric mean  ­it also indicates central tendency but uses product (pi)x instead of (sigma) x ­the geometric mean answers question if all numbers in a data set had same value what would  that value be


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