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Lecture 2

Lecture 2 - Frequency Distribution and Measure of Central Tendency + Variability - September 20

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Kristie Dukewich

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September 20, 2012. Lecture 2 – Frequency Distribution and Measure of Central Tendency + Variability Interpreting the Whole Group’s Data  Frequency distribution allow us to see patterns in the data Consider a Correlational Design  Sample of 40 people using Human Subject Pool o N=40  Research question: Do people who are higher in conscientiousness have better memory for details?  Two measures o Questionnaire measures conscientiousness o Memory task (max score = 100)  Before correlation analysis, investigate distribution of memory scores Interpreting the Whole Group’s Data  How do we calculate a frequency distribution using intervals?  Step 1: Find the Rand of Scores o Range = Highest Score – Lowest Score  Step 2: Determine the Interval Width (i) o Assume we want around 10 intervals o Determine i (interval width)  i = Range/Number of intervals  i = 51/10  i = 5.1 o Round up for down as required  Step 3: List the Limits of Each Class Interval o Begin with the lowest interval  The lowest interval must contain the lowest score  The lower limit of the lowest interval must be evenly divisible by i  E.g., lowest score is 42 which is not evenly divisible by 5 so start with 40 o Lowest score is 42. What is the lowest interval?  38-43  40-44   40-45  42-47  42-48  Step 5: Obtain the Interval Frequency  3 Kinds of Frequency Distribution: o Relative Frequency Distribution  Indicates the proportion of the total number of scores that occur in each interval  Relative f = f/N (N=40)  E.g., f = 3  3/40 = .075 (.08) o Cumulative Frequency Distribution  The number of scores that fall below the upper real limit of each interval  Starting at the bottom interval add the frequency of the interval to the frequencies of all the intervals below it o Cumulative Percentage Distribution  % of scores that fall below the upper real limit of each interval  Cum % = (cum f/n)100 General Information on Graphing  Vertical Axis o Called Y Axis or Ordinate o Plot Frequency of Scores (Frequency Distribution) o Plot Dependent Variable (Results of Experiment)  Horizontal Axis o Called X Axis or Abscissa o Plot Score Values or Intervals (Frequency Distributions) o Plot Levels of Independent Variable (Experiment)  Both Axes Must Be Labeled  Both Axes should start at 0. If not, indicate with a break near the intersection Summarizing Data Using Graphs  Distinguishing 4 types of graphs  TALE is the SKEW  Positively skewed data points to positive numbers, negatively skewed data points to negative numbers o Bar graphs  Nominal or ordinal scale data  Separate bar on X axis for each category or rank  Bars do NOT touch  To reflect discrete nature of data  Height of bar (Y axis) indicates frequency of category o Histograms  Created when data are on an interval or ratio scale  Separate bar drawn along X axis for each class interval  Each bar begins and ends at the real limits of the interval  The midpoint of each class interval is plotted on the X axis  Height of bars (Y axis) indicates frequency of class intervals  Bars DO touch (to reflect continuous nature of data)  Frequency Polygon: same as histogram but with plotted points and line graph instead o Cumulative Percentage Curve  Y-axis = percentage  X-axis = upper real limit of the interval o …? Interpreting an Individual’s Score  What can a percentile tell us about a person’s score?  Interpreting Percentiles: o Imagine you took Graduate Record Exam (GRE)  Verbal reasoning: max possible = 180, min = 130  Quantitative reasoning: max = 180, min = 13
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