Which of the following statement is incorrect ?

Q: Which of the following statement is incorrect ?

Which of the following statement is incorrect ?

Question

Accepted Answer

The correct option is 3:
The statement "r' is significant if it is less than six times of standard error" is incorrect, and thus it is the correct answer to the question asking for the false statement. In statistics, particularly when testing the significance of a correlation coefficient ($r$), a common rule of thumb is used, known as the P.E. rule (Probable Error rule). According to this rule, a correlation coefficient ($r$) is considered statistically significant (or definite) if its value is more than six times the value of its Probable Error ($P.E.$). If $r$ is less than $P.E.$ it is considered insignificant, and if $r$ is between $P.E.$ and $6 \times P.E.$, it is considered possible but not definite. Therefore, the requirement for significance is that $r$ must be *greater* than six times the standard error (or Probable Error) for a high degree of confidence, not *less* than it.

The incorrect option is 1:
The statement "Perfect correlation is ±1" is correct. The coefficient of correlation ($r$) measures the strength and direction of a linear relationship between two variables. Its value ranges from -1 to +1. A value of +1 indicates perfect positive correlation, and a value of -1 indicates perfect negative correlation.

The incorrect option is 2:
The statement "Variance is the square of standard deviation" is correct. Standard deviation ($\sigma$) is defined as the square root of the variance ($\sigma^2$). Consequently, the variance is mathematically the square of the standard deviation. This relationship is fundamental to understanding measures of dispersion.

The incorrect option is 4:
The statement "Mean deviation is 4/5 of standard deviation" is generally accepted as an empirical relationship for a normal distribution. For a normal or approximately normal distribution, the Mean Deviation (M.D.) is often found to be approximately 4/5 or 0.8 of the Standard Deviation (S.D.). This is an empirical relationship used in applied statistics, making the statement generally correct in the context of standard statistical properties.