Notes for 1/23/15-1/28/15
Notes for 1/23/15-1/28/15 PSYC 3301
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This 7 page Class Notes was uploaded by Rachel Marte on Monday February 9, 2015. The Class Notes belongs to PSYC 3301 at University of Houston taught by Dr. Perks in Fall. Since its upload, it has received 163 views. For similar materials see Introduction to Psychological Statistics in Psychlogy at University of Houston.
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Date Created: 02/09/15
12315 Important Statistical Terminology Important Definitions the fieldA set of mathematical procedures methods and rules used to organize summarize and interpret information The set of all of the individuals of interest in a study the group of people you are interested in 0 Note The statistics derived from samples are applied to populations if they are representative we almost always work with samples and then generalize to populations A subset of the population intended to representative of that population the people you collect data from 0 Note Samples are usually chosen by random sampling so that they are representative Numerical values used to describe a population on the basis of a single or multiple measurements 0 Note These are the statistics of populations you may hear the term population parameters but that is somewhat redundant Numerical values used to describe samples 0 Note These are the rough equivalent of population parameters you may hear the term sample statistics but that is somewhat redundant The discrepancy between a sample statistic and a population parameter 0 Note However representative a sample is the statistics derived from it can never match the real population parameters 100 therefore there is always sampling error Used to summarize organize and simplify data Inferential StatisticsWays to draw conclusions about populations on the basis of samples 0 Note These tend to be the main focus of realworld Statistics and are more useful than descriptive statistics Characteristic or condition that takes different values or an element feature or factor liable to vary or change 0 Note Know the di erence between an independent variable IV and a dependent variable DV Relates to observed variables to see if there is a relationship 0 Note Correlation does not prove causation The correlational method is only interested in determining whether or not there is a relationship between variables not whether or not one variable causes another Manipulates and controls variables in order to study cause and effect relationships by observing effects on other variables allows us to begin to infer causation 0 Note The IV is the variable researchers manipulate and the DV is the variable researchers observe The purpose of a welldesigned experiment is to determine whether or not there is evidence that the IV causes the DV Scales of Measurement Nominal ordinal interval ratio 0 Contains measurements that can be categorized in some way just categories 0 Category names re ect not only qualitative differences but also rank order differences contains information about differences but not about the size of those differences 0 In addition to rank ordering it also has information about the size of the differences the intervals between categories are of equal size 0 Contains all the information interval scales have but also has a meaningful zero point 0 Note More information about these scales of measurement will be presented after the list of definitions is concluded Consist of separate indivisible categories used with nominal and ordinal scales 0 Note Examples of discrete variables include Outcomes of a coin toss heads or tails the number of cars in a parking lot the number of siblings students have etc Can be broken up into an infinite number of possible values that fall between 2 observed values used with interval and ratio scales 0 Note Examples of continuous variables include Height weight temperature etc Organized summaries of the number of scores in each category on the respective measurement scale Show percentages or proportions for each category used for nominal or ordinal scales Frequency distributions from nominal or ordinal scales separate bars represent that the scale consists of separate distinct categories Used for interval or ratio scales bars touch because categoriesvalues overlap Frequency distribution where points are connected Scales of Measurement There are four scales of measurement and each builds off the ones before it For example an ordinal scale would contain all the information a nominal scale has as well as whatever new information it possesses An interval scale would contain all the information that ordinal and nominal scales have as well as extra information From least complex to most complex the scales of measurement are Nominal Ordinal Interval Ratio A nominal scale is just an unordered set of categories identified only by name All it tells you is whether two individuals are the same or different Examples religious preference Christian Jew Muslim etc political party affiliation Republican Democrat Independent gender male female etc An ordinal scale is an ordered set of categories It tells you whether two individuals are the same or different but it also indicates direction It does not however indicate the size of the differences between categories we might know who finished 1 2nd and 3rd in a race but we don t know how far behind the person in 2nd place was or how close to winning the person in 3rd was Examples rank 1 2nd 3 ranked scales How happy do feel today on a scale of 1 to 10 etc An interval scale is an ordered series of equalsized categories In addition to containing the information in nominal and ordinal scales an interval scale also identifies the direction and magnitude of a difference This kind of scale gives units meaning For instance the distance between 2 and 3 inches is equal to the distance between 10 and 11 inches Examples time temperature Celsius or Fahrenheit distance etc A ratio scale is an interval scale where a value of zero indicates a complete absence of the variable In addition to containing the information in nominal ordinal and interval scales a ratio scale also has an absolute zero point For instance the Celsius and Fahrenheit scales do not have an absolute zero point but the Kelvin scale does Examples income if you have 0 you literally have no money height if you are 0 ft you have no height etc Note For the intents and purposes of this class interval and ratio scales are roughly equivalent and can be used interchangeably Despite this it is good to know the di erence between them An example of the differences between the scales of measurement using time Nominal measure of time ampm Categories with no additional information Ordinal measure of time Morning afternoon evening night Indicates order of occurrence but spacing between categories is uneven Interval measure of time analogue 12 hour clock 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9101112 Units have meaning di erence between 4 and 5 pm is the same as the di erence between 10 and I I am Ratio measure of time 24 hour clock 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Midnight is the absolute zero Proportions and Percentages Some methods of graphing and statistical techniques require the use of proportions and percentages Below are the equations for calculating them Proportion of individuals in a single category p g f Percentage p100 quot100 Where fthe number of individuals in a category nthe number of individuals in all categories 126 15 Notation Frequency Distributions and Central Tendency Math Notation Observations yield raw scores which are represented by X Y etc X is usually the independent variable and Y is usually the dependent variable The number of scores in a population is represented by N and the number of scores in a sample is represented by n Npopulation size nsample size 2 is a sigma and represent summation o For example 2 1 2 3 means to add 1 2 and 3 together 2 1 2 3 6 0 Summation comes before addition in the order of operations PEMDSAS Parenthesis exponents multiplication division summation addition subtraction Central Tendency Central tendency identifies a single score to represent the Whole distribution mean median or mode Mean The balance point of a distribution preferred for interval and ratio scales 0 Equations 0 Sample Mean 2 2 0 Population Mean u I nNthe number of data items in the samplepopulation I Zxsum of all data values 0 The mean is affected by outliers consider using a different measure of central tendency if there are outliers 0 Adding a new score to the set Will change the mean 0 Adding or subtracting a constant to each score Will cause the same thing to happen to the mean ex if you add 3 to each score in the sample the mean Will increase by 3 o Multiplying or dividing a constant by each score Will cause the same thing to happen to the mean ex if you multiply each score by 3 the mean Will be multiplied by 3 Median The midpoint preferred When the distribution has extreme scores outliers or When using an ordinal scale 0 Symbolized Md 0 Example Find the median 1 2 3 the median is 2 Mode The score With the highest frequency used for nominal scales 0 Symbolized Mo 0 Example Find the mode 1 1 2 3 the mode is 1 12815 Measures of Variability Variability refers to the spread of the number values in a data set 0 Measures the average distance between a score and the mean 0 Tells us how well an individual score represent the whole population Measures of Variability Range The distance between the largest score Xmax and the smallest score Xmin 0 Range Xmax Xmin Standard Deviation Uses the mean as a reference point and computes the average distance for each point from the mean 0 Equations 2 0 Sample standard deviation S 2 0 Population standard deviation 0 39 Note The term 2X 502 is also known as the Sum of Squares SS Sometimes the equation will look like this S so know what the SS stands for 0 Symbolized s or sd Variance The standard deviation squared 2 0 Sample variance 32 Eiff 0 Symbolized s2 Example 0 If X 4 3 6 8 9 what is s and s2 43689 o x so x6 5 O S 4623 626 628 62962 5 1 I S so 32 so sV65 so s255 s22552 so s2650
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