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Chapter 3

Chapters 3,4,5.docx

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Department
Psychology
Course
PS296
Professor
Max Gwynn
Semester
Winter

Description
January 14 & 16 th th Chapter 3: Displaying Data 01/21/2014 Collection of #’s – to be interpretable, must first be organized in some sort of logical order 3.1 – Plotting Data simplest way to reorganize data is to plot them in graphical form frequency distributions, histograms, bar graphs, stem-and-leaf displays Frequency Dist. – distribution where values of DV are plotted against their frequency of occurrence Real Lower Limit – point halfway between the bottom of one interval & top of the one below it Real Upper Limit – point halfway between the top of one interval & the bottom of the one above it Midpoint – center of the interval Histograms – collapse data into intervals Optimal # of intervals to use when grouping data follows the: Goldilocks Principle – neither too many nor too few 3.3 Reading Graphs Histogram DV is on X axis Frequency on Y axis Bar Graph – frequency of occurrence of different values of X is represented by the height of the bar Uses vertical bards to represent whatever is being measured IV on X axis DV on Y axis Line Graph – Y values corresponding to values of X are connected by line - most important thing in making sense of a graph is to: first identify what is plotted on each axis identify IV & DV look for patterns 3.5 – Describing Distributions Symmetric – distribution with same shape on both sides of the center Bimodal – any distribution with 2 predominant peaks Unimodal – any distribution with only 1 major peak Modality – number of meaningful peaks in a distribution Positively Skewed – distribution trails off to the right Negatively Skewed – distribution trails off to left Skewness – measure of the degree to which a distribution is asymmetrical Chapter 4: Measures of Central Tendency 01/21/2014 Central Tendency – measures that relate to the center of a distribution of scores Chapter 4: Measures of Central Tendency 01/21/2014 4.1 – The Mode (Mo) least useful measure most common score is the value of X – the dependent variable that corresponds to the highest point on the distribution Modal Interval – 1.50-1.59 occurred 50 times (most common interval) If two adjacent times occur with equal frequency Take average of the 2 values  mode If two nonadjacent times occur with equal (near equal) frequency – bimodal distribution (2 distinct peaks) 4.2 – The Median (Mdn) middle score in an ordered set or data th 50 percentile Median Location – location of the median in an ordered series (N+1)/2 4.3 – The Mean (X)  X bar OR (M) Chapter 4: Measures of Central Tendency 01/21/2014 most common measure of central tendency known as the average the sum of all scores divided by the number of scores in the data mean & median are same in number when the distribution is symmetric nearly symmetric and unimodal distribution – mean, median, mode same Asymmetric Distributions – different mean, median, mode 4.4 – Advantages & Disadvantages of Mean, Median, Mode Mode Score that actually occurred Advantages Represents the largest number of people having same score Applicable to nominal data Disadvantages Depends on how we group data Not representative of the entire collection of numbers Median Advantage Major – unaffected by extreme score Doesn’t require any assumptions about the interval properties of the scale Disadvantage Chapter 4: Measures of Central Tendency 01/21/2014 Major – does not enter readily into equations More difficult to work with than mean Not as stable from sample to sample Mean Advantage Gives a more stable estimate of the central tendency of a population Can be manipulated algebraically Disadvantages Influenced by extreme scores Value may not exist in the data Interpretation requires at least some faith in the interval properties of the data Trimmed Means Mean that results from trimming away a percentage of the extreme observations Usually 10% or 20% from each side Used to eliminate extreme scores Common in treating skewed data For a 10% trimmed mean, we would set aside the largest 10% and smallest 10%  remaining mean would be the 10% trimmed mean Chapter 5: Measures of Variability 01/21/2014 Dispersion (Variability) – degree to which individual data points are distributed around the mean The difference in variability is a focus Groups could have different levels of variability even if the means are comparable 5.1 – Range Range – measure of distance (from lowest to highest score) Will suffer if there are unusually extreme values that stand out in the data set (outliers) 5.2 – Interquartile Range & Other Range Statistics Interquartile Range – the range of the middle 50% of the observations Is obtained by discarding the upper & lower 25% of the distribution & taking the range of whatever remains The range of a 25% trimmed sample The difference between 75 & 25 percentile Plays important role in graphical method  boxplot Trimmed Samples – samples that have a certain percentage of the extreme scored removed from each tail Trimmed Statistics – statistics calculated on trimmed samples 5.3 – Average Deviation (X-X)  deviations Chapter 5: Measures of Variability 01/21/2014 positive & negative deviations will balance each other out (sum of the deviations will always equal to 0) 5.4 – The Variance to eliminate the problem of (+)/(-) deviations balancing each other out would be to use absolute deviations – simply removing the sign in front of the deviation Variance is one of the most commonly used statistics Sample Variance (S2) – sum of the squared deviations about the mean divided by N-1 Divide by N-1 because it leaves you with a sample variance that is a better estimate of the corresponding population variance A different approach to the problem of the deviations averaging out to 0 Population Variance (Q2) – variance of a population; usually estimate, rarely computed Take advantage of the fact that the square of a negative number is positive We sum the squared deviations rather than the deviations themselves We then divide the sum by a function of N 5.5 – The Standard Deviation Standard Deviation – the positive square root of the variance; (s) when used in a psychological report, the symbol SD is used the notation Q is used only in reference to a population standard deviation always round to 2 decimal places how many scored fall no more than a standard deviation above or below the mean Chapter 5: Measures of Variability 01/21/2014 For normal distribution, approx. two thirds of observations lie within one standard deviation of the mean 5.6 – Computational Formulae for the Variance and the Standard Deviation Computational Formulae (Calculational) Algebraically equivalent to definitional formula’s, but require less effort EX – sum of all sc
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