Statistical methods and data interpretation

Statistical Methods & Interpretation of Scores:

Need statistics in educational evaluation:

1.                  To know students achievement

2.                  To know overall school achievement

3.                  To improve quality in education

4.                  To find out the status in education through educational research

5.                  To understand the data and drawing conclusion

Importance of Statistics in Educational Evaluation:

1.      To study students average attendance

2.      To study the comparison of result among individuals

3.      To study the comparison of result between two groups

4.      To study the correlation between two groups

5.      To study the position of student in group in terms of the percentage of individual which are below him.

Tabulation of Data:

1.      To understand the nature of acquired data

2.      To accept them data are to be organized. Three methods to organize data:

-         Classification

-         Tabulation

-         Presentation in graphic form

  Scores are organize in three ways:

-         Simple Array

-         Frequency Array

-         Frequency Distribution

A)    Simple Array:

1.      Simplest way to organize data

2.      Used when number of scores is small (20)

3.      Not used for repeated scores in obtained data

4.      Scores are arranged in ascending & descending order.

Example:

Raw scores                        Ascending order                       Descending Order

6                                        10                                            2

8                                        9                                              3

5                                        8                                              4

4                                        6                                              5

2                                        5                                              6

9                                        4                                              8

10                                      3                                              9

B)    Frequency Array:

Repeated scores in obtained data

Example:

Scores of 20 individuals age is given below

13,12,12,12,12,11,11,11,11,11,11,11,11,10,10,10,10,10,9,9

These scores can be organized in the following way

13

12,12,12,12

11,11,11,11,11,11,11,11

10,10,10,10,10

9,9

Above information is not clear

Thus better way to organize data is

Age                                          Tallies                                       Frequencies

13                                            |                                               1

12                                            | | | |                                          4

11                                            | | | | |    | | |                                8

10                                            | | | | |                                        5

9                                              | |                                              2

                                                                                    __________

                                                                                    N = 20                        

C)    Frequency Distribution:

An organization of measures or observations into score classes along with the frequency in each class is called frequency distribution.

Frequency distribution method is used when number of scores is too many. Scores repeated several times. Observations are divided into subgroups. Frequencies are depicted in front of each sub group

Steps for preparing frequency distribution:

1.      Find out highest & lowest numbers & difference between these two scores i.e. range

Formula is Range = Highest score/ number – Lowest score / number

2.      Determine number of class interval. It should between 5 to 20 depending on the range of scores.

3.      Determine size of class interval. It should be neither too big nor too small. Should be in odd number if possible.

Formula Size of class interval = Range / No .of class interval

4.      Determine number of class interval.

Formula No. of class interval = Range / Size of class interval

5.      Scores arranged in the classes

6.      Prepared class interval in such a way that the lowest number of scores should be the midpoint of first class interval.

7.      Limit of class interval should be multiple of 5

8.      Add size of class interval to each value of the first class interval, the next class interval can be obtained.

9.      Class intervals can be written in either ascending or descending order.

10.  Mark tallies against each class interval.