PSYC204-Lecture#4

PSYC204-Lecture#4

1. frequency distribution

   • def
   • bivariate f. distribution
     • you are measuring two things
   • to construct a f. distribution
     • Decide on number of classes
       • Convention: if there is a decimal or fraction you round down (number of classes)
       • Chose a starting point
         • What is going to be the start point of your classes, and what is going to be your end point convenient start point (i.e. little less than shortest student )
         • Calculate the class interval
     • example
       • Constructing a Frequency Distribution for the Height of the Statistics Class  1. Size of the sample: N= 140 (140 students )  2. square root N = square root(140 ) = 11.8 3. we can round it up (but we don't want to choose data that has intervals between it, therefore we round down; number of classes = 11) 4. Minimum (x) = 145  5. starting point= 145- 0.5 = 144.5 (take half a step backward) 6. Check data to see if there any other number that has a fraction. This is important in deciding what your starting point will be. You need to test that no other data has a decimal: for example if one of your data points was 162.1cm, you have a 10th decimal place, you subtract to the 100th decimal place.   (162.1 -> 145 - 0.05 = 144.95) If your starting point is 162.12cm, to the 100th place you subtract from the 1,000th place: (162.12 -> 145 - 0.005 =  144.995 )     7. max (x) = 197 8. stop point = 197-0.5 =197.5 9. Class interval = (end point - start point)/ # of classes = ( 197.5 - 144.5 ) / 11 = 4.8 ~ 5

2. Descriptive Statistics

   • percentile
     • Def: If you order the data from smaller to largest percentiles, divide ordered data into hundredths, for example, the 30th percentile is the score that 30% of the scores are the same or lower than that score  
   • median
   • quartile
     • Quartile are special percentiles: Q1= 25% percentile, M=50% percentile, Q3 = 75th percentile.   The point that divides the distribution into quarters. Procedure: rank order scores: find the median. Q1 is the median of the lower half of the data and Q3 is the median of the upper half of the data.    
   • measures of central tendency
     • mean
       • you add all the heights together and divide by the number of students
     • median
       • 50th percentile (half of the data has a score less than or equal to median) is the point that divides the distribution, equal number of scores above and below, “centre of data”  
       • midway through data, mid-point rank order
       • Ex
         • Case 1: 1,1, 3, 4, 5 N=5 obs. (N+1)/2 =3 (rank of median) 
     • mode
       • most common

3. Graphical Representation

   • Bar Chart:
     • Bars are separated from each other, frequency is represented by height of the bar, total height (of all the bars added together?) = number of measures = net f = N  
   • Histogram
     •  f. is represent by area, more area means greater f., total area = number of measures = net f. = N, on y axis you put frequency (this comes to play when we consider mean), good part of the histogram, part of the area = number of measures in the interval (i.e. chequered area on the left = # of measures = 24, dark area on the right = 13); portion and percentage can be displayed in a similar manner by showing proportion and %
     • Relative Frequency (%F) Histogram
       • area = relative f. (%) total area = 100% Proportion of area = proportion of measures ( or %) in the designated interval(s) the light area = proportion of sample 159.5 < x < 169.5
   • Frequency Polygon
     • The line joining the midpoints of the class intervals in a histogram