ED 602

Statistical Research for Behavioral Sciences

Brian G. Smith, Ph.D.
Lesson 4 - Frequency Distibution, Percentile Ranks, Graphing

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Homework - Lesson 4

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Assessment - Lesson 4

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Assignment and Information

Reading: Chapter 2
   Definition Page: Contains definitions arranged alphabetically.

Notes

Describing data

  • Raw data
    • is disorganized
    • is difficult to understand and remember
  • Frequency distributions - shows how often something occurred during a study
    • Ungrouped – uses all possible scores
    • Grouped – uses class intervals
    • Each score can fit only one class interval
    • Each interval should be the same distance
    • Use 6-15 intervals to get the information across without adding confusion
    • Base intervals on categories that make sense for your data
    • Try to avoid open ended intervals
  • Variations of frequency distributions
    • Cumulative frequency distributions – shows the number of scores from this point and lower
    • Relative frequency distributions – shows proportion of total scores
    • Percent frequency distribution – the relative frequency distribution times 100 so the score can be reported as a percent
    • Cumulative relative frequency distribution – shows the proportion of scores from this point and lower, this number times 100 is a rough estimate of the percentile rank if there are not duplicate scores.
    • Percentile rank – the percentage of scores in a distribution that are equal to or less than that score. The cumulative relative frequency times 100.
  • Histograms – a form of bar graph in which the frequency of a score in a class interval is given by the height of the bar
  • Stem and leaf displays – a display of the data in shich the first or second digit of a score is the stem and the second or last digit is the leaf
  • Bar graph – used to present frequency distributions when the variable is qualitative in nature.

Shapes of frequency distributions

  • Symmetry
    • symmetrical – if folded in half at the midpoint, both halves match
    • asymmetrical - if folded in half at the midpoint, halves don’t match
  • Skewed distribution – scores cluster at one end of the distribution
    • Positive skew – scores cluster at the low end of the scale
    • Negative skew – scores cluster at the high end of the scale
  • Modality
    • Unimodal – only one score occurs most frequently
    • Bimodal – two scores occur most frequently
    • Multimodal – multiple scores occur most frequently

Now we can use this information to look at our BASC data.

1. These are the scores you collected for the Hispanic students in your BASC study:

 

25        40         45         50         52        

55         59         63         73         32        

41         48         51         52         55

60         65         37         44         49

51         52         57         62         67
2. An ungrouped distribution would look like this:
3. A grouped distribution might look like this:
4. A grouped frequency histogram would look like this.

SPSS Tips:

 

Once your histogram is drawn, you can adjust the class intervals by double
clicking on the graph, then clicking on the numbers under the smaller graph
that comes up in the chart editor. Change the intervals to custom, then
define your new intervals.

Vocabulary

Raw data - The scores of a subject exactly as collected and before they are analyzed statistically.

Frequency distributions - A table showing each score in a set of scores and the number of times it occurred

  • simple ungrouped frequency ( f )   - Listing each possible score value and then placing a tally mark next to each score for each time it occurs in a set of scores results
  • relative ungrouped frequency ( rf ) - Dividing the frequency of a score by the total number of scores in the distribution of scores
  • percent ungrouped frequency ( % f ) - the relative frequency ( rf ) scores multiplied by one hundred.
  • simple grouped - Listing each possible class interval and then placing a tally mark next to the interval for each time a score in that interval appears in the set of results. 
  • relative grouped - Dividing the frequency of scores in an interval by the total number of scores in a grouped frequency distribution
  • percent grouped - the grouped relative frequency multiplied by 100

Class interval - the range of score values into which the raw scores are grouped in a grouped frequency distribution.

Cumulative frequency of a score -( cf ) - the frequency of occurrence of a score plus the sum of the frequencies of all the scores of lower value.

Percentiles - a score at or below which a specified percentage of the scores ina distribution fall

Percentile rank - the percentage of scores in a distribution that are equal to or less than that score

Histograms - a bar graph in which size of the class interval is represented by the width of the bar on the abscissa (x axis). and the frequency of scores in the class interval is given by the height of the bar.

Frequency polygons - Connected dots indicating the frequency at the midpoints of classintervals with straight lines

Stem and leaf display - A display of data in which the first digit of a score is the stem, and the last digit is the leaf.

Bar graph - a graph used to present a frequency distribution for qualitative data

Symmetrical frequency distribution - A distribution in which one side is the mirror image of the other side

Skewed - when a distribution has scores clustered more at one end than at the other

Mode - the most frequently occurring score in a distribution