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Lecture 2

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University of Toronto St. George
Kristie Dukewich

Lecture 2 Statistics, Sept 20  Operational definitions  When you are creating an object to measure, you want to be sure that if two people are measuring it, they will get to the same answer  Real limits: in chapter 2  Main concepts from Pagano Chapters 3 and 4  Interpreting a whole group`s data  Frequency distribution allow us to see patterns in the data  Correlational Design  Grouped Frequency Distribution  How to define  1. Find the range of scores  Highest score – lowest score  Find range  2. Determine the interval width  Assume we want around 10 intervals  Determine i (interval width)  i = range/number of intervals  Range = 51; intervals = 10  i = 51/10  i= 5.1  You have to round it to 5, so 10 intervals each with 5 units  3. List the limits of each class interval  Begin with the lowest interval  Must contain the lowest score  Must be evenly divisible by i  4. Tally the scores  5. Obtain the Interval Frequency  3 kinds of frequency distribution:  Relative Frequency Distribution  Indicating the proportion of the total number of scores that occurs in each interval  Relative f = f/N  N= 40 (40 data points)  f= frequency distribution  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  Example: If the first interval frequency is one, then add 1 to whatever the frequency of the second interval is  Cumulate Percentage Distribution  The percentage of scores that fall below the upper real limit of each interval  Cumulative percentage = (cum f/n)100  So cumulative frequency, divide it by the # of scores, and times it by 100  They are always one or less than one!  Summarising data using graphs  Vertical axis = y axis = ordinate  Frequency of scores (frequency distribution)  Plot dependent variable (results)  Horizontal axis = x axis – abscissa  Plot score values or intervals frequency distribution)  Plot levels of independent variable (experiment)  Both axes must be labeled  Both should start at 0, and if not indicate a break near the intersection  Distinguishing 4 types of graphs  Bar graphs  Nominal or ordinal scale data  Separate bar on X axis for each category or rank  Bars do NOT touch  Reflects the discrete nature of data  Histograms  When data are on an interval or ratio scale  When distance between units are constant  Separate bar drawn from 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 pl
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