DESCRIPTIVE STATISTICS

Goal of descriptive stats: To simplify the organization & presentation of data

            Several techniques are used for this:

                        Some kind of summary graph or table that makes patterns easier to see

Some kind of measure of an “average” or “typical” score

                        Some kind of measure of how different the scores are – how “spread out” they are

Frequency distributions, either in tables or graphs – are very common tools for simplifying information and making it easier to see patterns.

In the following example it is very difficult to see a pattern.

Table 2-1  (p. 35)
Memory scores for a sample of 16 participants.  The scores represent the number of sentences recalled from each category.

One way to summarize the data could be in the form of a Figure, shown below. We will discuss how to construct such figures later.

Frequency Distribution Table

An organized tabulation of the number of individuals located in each category on the scale of measurement.

Frequency distribution tables: usually list scores from highest to lowest.

Construction of Frequency distribution tables:

            List the categories (the X-values) from the scale of measurement in a column

            Beside each value a second column indicates the # of times (frequency) each value occurred

            A third column may indicate the proportion (relative frequency) for each value

                        Proportion :   p = f/n where f = frequency, N = total number of cases.  Proportion is also known as relative frequency.

            A fourth column may include percentages for each value

                        Percentage:  p x 100   or    (f/n) x 100

We will discuss in class ways of calculating SX the sum of all the scores in a set of data, from the Frequency Distribution table.

GROUPED FREQUENCY DISTRIBUTION

Often used when data have a wide range of values

            Advantage – improves management and presentation of data

            Disadvantage – specific information regarding individual scores is lost  

·        Establish class interval

a.       The number of intervals should be 10-20.

b.      Choose a convenient interval size (e.g. 3, 5, etc.)

c.       The lowest score should be a multiple of the width [e.g., if the lowest score is 44, and the interval width is 5, then start with 40, not 44]

d.      Be aware of the actual interval size (with real limits, in the case of a continuous scale)

When f is a whole number, the number of rows can be obtained by finding the difference between the highest and lowest scores and adding 1.

E.g. (98-30) + 1 = 69               69 divided by 5 = approx. 14 intervals

Once the intervals are established, list them in a column and then add a column of frequencies, etc.

Example 2.3 (p. 40)

82        75        99        93        53        84        87        58        72        94        69        84        61        91        64        87            84        70        76        89        75        80        73        78        60

The following is an example of a grouped frequency distribution based on these data.

Table 2.2  (p. 41)
A grouped frequency distribution table showing the data from Example 2.3.  The original scores range from a high of X = 94 to a low of X = 53.  This range has been divided into 9 intervals with each interval exactly 5 points wide.  The frequency column (f) lists the number of individuals with scores in each of the class intervals.