PSY 211 Week 2
PSY 211 Week 2 Psych 2110
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This 3 page Class Notes was uploaded by KhloNotes on Monday September 5, 2016. The Class Notes belongs to Psych 2110 at University of Alabama - Tuscaloosa taught by Andre Souza in Fall 2016. Since its upload, it has received 9 views. For similar materials see Elem Statistics Business in Psychology (PSYC) at University of Alabama - Tuscaloosa.
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Date Created: 09/05/16
Key: Bold/Italic = important information, Highlighted = vital for test From 211 Elementary Statistical Methods (Psychology) ; Professor Souza Ideas Stressed in Chapter Two: Measurements often cluster around certain values Data Frames: An object w/ rows and columns used for data collection and organizing data Rows contain different observations Columns contain the values of different variables Values can be quantitative (numbers) or text (qualitative) Sum of Squares ̄ or Σ (xi x) (Most important measure in Statistics) Central Tendency Shows the typical observation for a given variable Different samples will be different because everything varies, but sample statistics also cluster around central values Arithmetic Mean Most straightforward Represented by a letter w/ a bar on top: x ̄ Sum of all data points divided by the # of data points n ̄ Formula: x = (Σx)/n Answers: If all the data points had the same value, what would that value be? Can replace every number in the data set and still equal sum Only appropriate for quantitative variables Sensitive to outliers Properties of Mean Usually pulled in the direction of the outlier For binary data, the mean equals the proportion of observatory equalling 1 Arithmetic mean is the only single number for which the residuals (as defined as the distance between each data point and the mean) sum to zero ̄ Formula: Σ(xi x ) = 0 Best estimate for the value of a group of numbers Geometric Mean For process that change multiplicity rather than additively Uses product (Πx) instead of sum (Σx) n ̄ Formula : x = Πx Key: Bold/Italic = important information, Highlighted = vital for test Good for numbers that are not independent of each other Median Middle value in the dataset (number separating the higher and lower halves of a distribution) Arrange values low to high and cross outside numbers off until you reach the middle term OR take number of terms and add by 1 then divide by 2 For lists where the middle term is a decimal or even numbered, add the middle two terms and divide by 2 Not sensitive to outliers Median Properties Appropriate for quantitative and and ordinal variables Requires ordered data Not affected by outliers = appropriate for skewed distributions Mode Represents the most common outcome (frequency) Can be used for categorical and numerical variables Note: Be aware of which variable the question is requesting Measures of Variability (VERY IMPORTANT) What is variation? The greater the variability in your data, the greater your uncertainty Range Distance covered by the scores in a distribution, from smallest and largest Distance between between the minimum and maximum values ̄ Distance between each data point and the mean ( xi x) s called residual, deviation, or error Then, take distance mean and add them all up before dividing by n ̄ Formula: Z (xi x) / n The answer should always be zero Useful for finding the mean and seeing how far from the mean each data point Key: Bold/Italic = important information, Highlighted = vital for test Residuals Sum will be zero or close to zero due to rounding errors Negatives cancel out positives ̄ Σ | xi − x ̄| or Σ (xi x) to get rid of negatives Represents the total variability in a data set Characteristics: Always the squared of the original unit The more numbers, the bigger the Sum of Squares (SS) Avoidable if you divide the SS by the sample size, resulting in a Average Sum of Squares or the Variance Variance Σ (xi − x)̄ Formula: n Computational Formula: Measured in squared units Degrees of Freedom “n1” Allows us to make inference w2 room for error Σ (xi − x)̄ est requires n − 1 f Squared Deviation 2 Formula: Σ (xi − x)̄ √ n − 1 Computational Formula:
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