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PY 211 Lectures 1-10

by: Jennifer Scheuer

PY 211 Lectures 1-10 PY 211

Jennifer Scheuer
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About this Document

My notes from Lectures 1-10.
Elem Statistical Methods
Andre Souza
Class Notes
Psychology Statistics, Statistics




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This 7 page Class Notes was uploaded by Jennifer Scheuer on Saturday February 6, 2016. The Class Notes belongs to PY 211 at University of Alabama - Tuscaloosa taught by Andre Souza in Spring 2016. Since its upload, it has received 76 views. For similar materials see Elem Statistical Methods in Psychlogy at University of Alabama - Tuscaloosa.


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Date Created: 02/06/16
PY 211-Introduction to Statistical Modeling (Chapter 1) What is Statistics? The science of learning from data, and of measuring, controlling, and communicating UNCERTAINTY. Gives methods for analyzing, collecting, and making predictions based on data. Statistics quantifies variation. Variation Everything varies. Statistically Significant: if the variation observed is larger than expected. Non-Statistically Significant: if the variation observed is what one would expect. Something (an explanatory variable) is influencing (changing the variation of) what we are observing (the response variable) Variables Response variable: the variable whose variation you are trying to understand. Explanatory variable: the variable that is influencing the variation of the response variable. Variable: something that takes up different values. (the label not the actual value) Key Terms in Statistics Descriptive Statistics: the summary of the information in a collection of data. Inferential Statistics: using sample statistics to estimate the values of population parameters. Population: the total set of units. Sample: a subset of the population. Parameter: a number that describes the entire population (represented by greek letters) Statistic: a single number that summarizes a sample (represented by roman letters) Random Sampling: each member of a population has to have an equal chance of being selected as part of the sample. (Ex. Testing soccer players, but draw from a population of baseball players) Parameter Estimation: using a sample to guess the population. PY 211-Basic Concepts in Statistics (Chapter 2) Types of Variables Discrete Variables: variables that can only take on specific values. (Ex. Number of siblings) Continuous Variables: variables that can take any real number value. (Ex. Reaction time) Categorical Variables: qualitative variables, used to characterize a set of categories. They can be: Nominal: two or more categories where order does not matter. (Ex. Modes of transportation) Dichotomous: only two categories where order does not matter. (Ex. True or false) These are also nominal. Ordinal: two or more categories where order does matter. (Ex. Rankings) Quantitative Variables: variables characterized by numerical values. They can be: Interval: numerical values in which the intervals between the values are assumed to be the same. (Ex. Temperature) Ratio: numerical values with a meaningful zero point. (Ex. Height) Zero represents the absence of a variable Understanding Types of Variables All categorical variables are discrete. Quantitative variables can be either continuous or discrete. PY 211-Displaying Data (Chapter 3) Data Summary  Categorical Variables: list the categories and show the frequency for each category.  Frequency Distribution: the listing of possible values for a variable with the number of observations at each value.  Relative Frequency: the proportion or percentage of observations that fall in the particular value.  Outliers: extreme observations that fall far from the rest of the data. (cause exaggerated estimates) PY 211-Measures of Central Tendency (Chapter 4) Data Frames Object with rows and columns. Rows contain different observations. Columns contain the values of the different observations. The values can either be quantitative or qualitative. Central Tendency The tendency of measurements to cluster around certain values. Sample statistics often cluster around central variables. Find it by plotting data. Mathematical Notation A variable will be represented by a lowercase letter. Individual values of a variable are represented by a subscript. To refer to a since value without specifying which one it is use xi  Σ means to sum everything that follows. Arithmetic Mean The most straightforward measure of central tendency. Represented by x . Answers the question of if all the data points had the same value, what would that value be? Only works for quantitative variables. It is very sensitive to outliers. Only single number for which the residuals sum to zero: ∑ x −x´ =0 ( i ) Geometric Mean Answers the question of if all the numbers in a dataset had the same value, what would that value be in order to achieve the same product? Represented by ^  Used when numbers are dependent on each other: ^ = n∏ x √ Median The middle value in a dataset, separate the higher half from the lower half. Not sensitive to outliers. Have to arrange the numbers from lowest to highest and find the term in the middle. If there is an even number of values then the median will be the average of the two middle values. Appropriate for quantitative and ordinal variables. Mode Represents the most common outcome. Mostly used for highly discrete variables, but applicable to all types. PY 211-Measures of Variability (Chapter 5) Variability Measures how well an individual score represents an entire distribution. Greater the variability the greater the uncertainty about the parameter that is supposed to be estimated. Range The distance between the minimum and the maximum values. Only two data points contribute to the range (minimum and maximum) Residuals  The distance between each data point and the mean.  The longer the residual line the more variability in the data.  The sum of all the residuals will be zero.  To get rid of the negative signs take the absolute value or square the residuals. x −x  Absolute Value: | i | ) ∑¿  Square: ∑ (xi−x´) Sum of Squares 2  Square: ∑ (xi−´) = SUM OF SQUARES  Sum of the squared deviations. 2  Computational formula: ∑ x − (∑ x) n  Represents TOTAL VARIABILITY  The more numbers (the bigger the n) the bigger the sum of squares.  Have to make sum of squares NOT dependent on sample size. ∑(xi−´x)  Mean squared deviation: n Degrees of Freedom  The sample size minus the number of parameters estimated from the data.  We have (n-1) free choices if we estimate a parameter from a sample size n. Variance Provides an unbiased estimate of population variability. The sum of squares divided by the degrees of freedom. Measures AVERAGE VARIABILITY ∑(xi−x)2 Conceptual Formula: n−1 2 2 ∑ x) Computational Formula: ∑ x − n n−1 Measures the reliability of an estimate Standard Deviation  Conceptually the same as variance.  Variance is difficult to interpret because it is in squared units.  Resolve that problem by taking the squared root, which is the standard deviation. 2  Conceptual Formula: ∑(xi−x´) √ n−1 2 2 ∑ x)  Computational Formula: ∑x − n √ n−1  The typical distance from the mean.  Greater variation around the mean the greater the standard deviation.


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