Quantitative Methods 2317 Sect 001 Final Exam Study Guide Chapter 1 Displaying the Order in a Group of Numbers Two Branches of Statistical Methods 1 Descriptive summarize and describe a group of numbers from a research study 2 Inferential draw conclusions and make predictions Basic Concepts Variable any characteristic or condition that can change vary Gender age Value possible number or category a score can have Male female transgender 0 100 Score a particular person s value Female 86 Six Levels of Measurement 1 Equal Interval variable in which the numbers stand for approximately equal amounts of what is being measured a GPA difference between 2 3 and 4 0 difference between 1 7 and 3 4 b Depression scores on BDI difference between 5 and 7 difference between 2 and 4 2 Ratio special case of equal interval a Contains a true zero point value of zero absence of the thing being b Grades number of siblings distance time weight 3 Rank Ordered Variable Ordinal values correspond to number of things being a Standing in graduating class Valedictorian 530th b Place in a race 1st 2nd 3rd birth order 4 Nominal Variable Categorical names or categories gender diagnosis PTSD measured measured Schizophrenia a Ethnicity European American African American Latino a 5 Continuous possible to have an infinite number of values between two intervals a Height no way to measure every possible inch foot centimeter age you could be 26 932210 years old 6 Discrete values that have no other values between them a Number of siblings nominal variables gender religion etc Frequency Tables Table that shows how many times each score is used Nominal data taco burger football team Steps 1 Make a list of each possible value from lowest to highest 2 Go through scores making a mark for each value next to it 3 Make a table showing how many times each value is used 4 Calculate percentage of scores for each value Can be used for nominal variables can group intervals of variables together Histograms Height of each bar is the frequency of each value in the frequency table When you have a nominal variable the histogram is called a bar graph Steps 1 Make a frequency table 2 Put the values along bottom of the page left to right highest to lowest 3 Make a scale of frequencies on the left side of the page from 0 to highest frequency for any value 4 Make a bar for each value with a height for the frequency of that value Six Shapes of Frequency Distributions 1 Unimodal one high area hump 2 Bimodal two fairly high points humps 3 Rectangular Uniform values all have about the same frequency 4 Symmetrical left and right side of distribution are mirror images 5 Skewed score pile up on one side of the distribution not symmetrical a The side with fewer scores tail is the direction of the skew b Skewed to the right positive c Skewed to the left negative 6 Normal Curve distribution that is bell shaped symmetrical unimodal and Kurtosis how much curve differs from normal curve in terms of more peaked mesokurtic and more flat Three General Forms Leptokurtic positive highest peak more common Mesokurtic normal Platykurtic negative low peak less common Misleading Graphs failure to use equal interval sizes population data Exaggeration of proportions start at 0 to see actual proportions Central Tendency and Variability Chapter 2 Descriptive Statistics Central Tendency values clump toward middle Middle of a group of scores Variability spread out from middle Central Tendency Mean average of all scores Most common M X N Mode most common value in a distribution use of mean median and mode in psychological research Largest frequency Used with nominal variables Median middle score with numbers in order from lowest to highest Used with rank ordered variable and skewed Sometimes used when distributions have outliers score with an extreme value in relation to other scores Normal Distribution mean median and mode in similar place center Positively Right Skewed left to right mode median and then mean tail Negatively Left Skewed left to right tail mean median and then mode The amount of spread of the scores around the mean how close or far from the mean are the scores more spread out higher variability 2 methods variance SD2 and standard deviation SD Variability Variance Steps 1 Subtract the mean M from each score 2 Square each of these deviation scores 3 Add up the squared deviations scores 4 Divide the sum of squared deviations SS X M 2 by the number N of scores SD2 X M 2 N SS N Standard Deviation is the square root of the variance Inferential Statistics Chapter 3 scores below the mean Variance is calculated in squared deviations from the mean Most common way to describe a spread of scores is the standard deviation which Z Score takes into account both standard deviation and mean of a group of Describes a score in terms of how many standard deviations it is above or If the actual score is above the mean the z score is positive If it is below the mean the z score is negative Change raw score to z score Z X M SD Raw score given X Z x SD M Also known as a standard score A distribution of z scores will always have certain characteristics Mean 0 SD V 1 to z scores The shape of a distribution does not change when raw scores are converted If the distribution of raw scores is negatively skewed so will the Most variables psychologists study have distributions that are approximately distribution of z scores Normal Curve normal Characteristics Unimodal Symmetrical mesokurtic Bell shaped Shape of normal curve is standard mathematically perfect We can estimate the percentage of scores above or below a particular point 34 14 and 2 on either side total 68 28 68 28 96 4 68 28 4 99 Steps for figuring out the percentage of scores above or below a particular score Change raw score to z score Draw a picture of the area in question Sample and Population Normal Curve where the z score falls and then shade Population entire group of people to which a research intends a study to apply Sample scores of the particular group of people studied In research we usually study a sample but make inferences about a population Types of Sampling selected Random Selection each person in the population has an equal chance of being Haphazard Selection taking whoever is available biased need a system to get a representative sample Statistical Terminology Samples and Populations Population parameters Mean Standard Deviation Variance 2 Sample statistics Mean M Standard Deviation SD Variance SD2