PSYCH 210 1st Edition Lecture 3 Outline of Last Lecture I. Ways of Using Variables in Researcha. Correlational MethodII. Scales of Measurementa. Nominalb. Ordinalc. Intervald. Ratio ScaleIII. Discrete vs. Continuous DataIV. Summation NotationOutline of Current Lecture I. Finish Summation NotationII. Frequency DistributionsIII. GraphingIV. Percentiles and Percentile RanksCurrent LectureI. Summation Notation (Continued)a. Σx2 means square first, sum second vs. (Σx)2 means sum first, square secondi. These two rules are NOT equivalent!b. Rule 6: Adding a constant to every score These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.i. Σ(x+C) = Σx + nCc. Rule 7: Multiplying every score by another variable (Rule 7)i. Σ xyii. Multiply first, sum secondd. Rule 8: Multiplying the sums of two variablesi. (Σx)(Σy) or ΣxΣyii. Sum first, multiply secondII. Frequency Distributions (FDs)a. They are a method for summarizing data (Descriptive Stat)b. Simple Frequency Distributions (SFDs)i. Two columns: x (raw score) and f (frequency)ii. Rank order scores (normally from highest to lowest)iii. Sum of frequency (f) column must = n (total number of scores)iv. **Must include ALL x values, even if they ‘don’t exist in data set!’ 1. If raw score d.n.e., f=0c. Grouped FDs (GFDs)i. Condenses Information1. Makes it easier (faster) to read data2. Less detaileda. Ex) No longer know for certain the lowest or highest valuesii. No definite rules for creating (the following are ‘guidelines’ for creating GFDs)1. Determine total number of rows you would need for a SFD a. SFD rows = Highest – Lowest + 12. Determine number of class intervalsa. Normally want ~103. Determine width of class intervalsa. (Total # of rows)/(# Class Intervals) = Class WidthIII. Graphinga. Class example: Babies Babbling, form of practicing languagei. Sonogram and Video Recordingb. Histogramsi. Like Bar Graphs but used only with Continuous data1. No gaps between barsii. Using GFDs1. y axis: Frequency, x axis: midpoint of group intervalc. Frequency Polygonsi. Top of Bars (in Histogram) become pointsii. Add two categories (one on each end of data set) in order to connect line to x-axisiii. With lots of data points, line becomes smoothd. Bar Graphsi.Only used for discrete data1. Gaps between bars (unlike in Histograms)e. Line Graphsi. Connecting dots (without connecting to x-axis)ii. Helpful for time plotsf. Graphs can be misleading!i. Can manipulate them to make them look the way you want them to!g. General aspects of graphsi. Symmetry1. Degree to which graph can be folded in half and the halves are mirror images of each otherii. Skew1. Degree to which graph is off symmetry2. Positive and Negativea. Tip for Remembering: depends on which way the tail is pointingb. Ex) Positive Skew: Number of Children Born in US Households or Incomec. Ex) Negative Skew: Exam that was too easyd. *The type of data you have affects type of stats you can perform (inferential)iii. Modality1. Mode = Most common score (peak of your curve)2. Symmetrical, Unimodal3. Symmetrical, Bimodal4. +Skew, Bimodal5. No modeIV. Percentiles and Percentile Ranksa. What can these stats be used for?i. Relative Standing in a distributionii. Ex) Standardized tests 1. SAT, ACT >> ‘89th percentile’iii. Percentile tells where a point falls relative to all the other pointsb. Relative frequenciesi. Useful for understanding smooth curvesii. Frequency divided by Total number of scores 1. f/nc. Cumulative Frequencies (Cf)i. Needed to calculate percentilesii. Add up frequency starting from the bottom1. Last Cf value calculated = nd. Cumulative Percentage (C %)i. Divide each Cumulative frequency by n1.