SCORE
THE Z- SCORE
It is a statistical tool which determines whether there is any dependence or correlation among two or more variables. Z score is closely related to the p- value which is the probability that the null hypothesis will be rejected. The Z scores can be represented in a graph of standard normal distribution that is the standard deviation against probability. When the Z score is very high or very low, this is often associated with very small p- values; they are normally situated in the tails of the distribution curve
An illustration on the application of z-score can be explained in a research involving the evaluation of teacher effectiveness and student performance. The z score will indicate whether teacher's effectiveness affects student performance. The students can perform very well or poorly depending on the effectiveness of the teacher. Educators can use this method to decide on which mode of teaching is effective to a particular group of students to achieve desired results.
The formula for calculating Z score is:
Z = (x-µ) / ? Where:
Z = The Z- score
X = The raw score
µ = The mean of the population
= Standard deviation of the population
When the Z -- score value gives a negative score, it means that the teaching strategy has an effect on the performance of the students that is to say that there is a correlation between student performance and teacher effectiveness. This can be translated to mean poor teaching strategies will mean poor performance by the students. When the Z- score is positive it means that the teaching strategy has no effect on the performance of the student. That is to say a change in the teaching strategy will not affect the student performance. The Z score majorly tells us how far a given set of data is from the mean; this distance from the mean is basically measured in terms of standard deviation. If for example, a variable has a Z score of -0.0849. This means that it is 0.0849 standard deviations below the mean, if the Z score is +0.0849 then it means that it is 0.0849 standard deviations above the mean.
Variables
Variables allow the researcher to maintain control of the research process quantitatively. The dependent variable is that variable that changes when the independent variable changes. In the above example the variables are as follows
Teacher effectiveness- independent variable
Student performance -- dependent variable
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