Tuesday, November 14, 2023

DERIVED SCORES ZSCORE T SCORE STANDING SCORE



Derived Score Z Scores
 T score Standing Score

Derived scores like Z score, T score and standing score are statistical measures used to standardize and compare data. z score is the standardization from the population raw data or more than 30 sample data to a standard score, while the t score is the standardization from the sample data of less than 30 data to a standard score. z score ranges from -3 to 3, while the score ranges from 20 to 80.

 

Z score

A z score measures how many standard deviations a data point is from the mean of a group of data. It helps to understand where a particular data point stands within a distribution.

If raw score = mean Z score is zero

If raw score > mean Z score is positive

If raw score < mean Z score is negative.

 Advantages of Z score

·         standardization

·         comparison and ranking

·         used for normal distribution

·         probability calculations

·         threshold identification

·         comparing different scales

·         data transformation

 

Limitations of Z score

·         assumption of normal distribution

·         sensitive to outlier

·         dependence on sample size

·         assumption of interval or ratio scale

·         interpretation  complexity

·         not robust against skewed data

·         dependency on parameters

Types of Z score table             

·         positive z score

                      The observed value is above the mean of total values.

·         negative z score

                   The observed value is below the mean of total values.

T score

 

T-scores are similar to z-score but are used when the sample size is small. They represent the number of standard deviations a data point is from the mean, considering the smaller sample size. It indicates how many SD units an examines score is above or below the mean

Advantages of t small size sample     

·         flexibility in hypothesis testing

·         accommodates  unknown parameters

·         reduced sensitivity to outlier

·         wider applicability

·         accurate in non normal distributions

·         adjustments for degrees of freedom

·         commonly used in research

·         scores

Disadvantages of t score                                                          

·         sensitive for assumptions

·         impact of outlier

·         requires random sampling

·         dependence of equal variances

·         cautious interpretation with small sample size

·         type 1 error risk with multiple testing

·         assume interval or ratio data

·         limited to comparing means

·         assume independence

Types of t score

·         one sample t test

       This test compare data to a theoritical mean

·           two sample t test

                This compare the means of two  group of data

·         paired t test

                    This test compare the mean of the same data group changes

Standard score

This is a generic term for score that have been standardized to have a mean of 0 and a standard deviation of 1 .both z score and t score are types of standard scores.

Formula for calculating z score t score

Z score

z = (x - /mu}{/sigma)

z = Z score

x= individual data point

/mu mean of the distribution

/sigma standard deviation of the distribution

This formula provided a standardize measure of how far a data point is from the mean in terms of standard deviation.

T scores

t = (x -/bar {x} {s/{n})

t =t score

X sample mean

/bar {x} population mean

s sample standard deviation

N sample size

This formula assesses how far the sample mean deviates from the population mean in term of standard errors

Z score and t score are both used in hypothesis testing

Key Differences between Z score and t score

Z| score

T score

Standardization from population data

Standardization from sample data

Population is known

Population is not known

Average is always zero

Average is always 50

It ranges from -3 to 3

It ranges from 20 and 80

Standard deviation is always 1

Standard deviation is always 10

The derived result can be negative

The derived result can never be negative

 

 

 









     PPT PRESENTATION




No comments:

Post a Comment

DERIVED SCORES ZSCORE T SCORE STANDING SCORE

Derived Score Z Scores  T score Standing Score Derived scores like Z score, T score and standing score are statistical measures used to s...