Statistics (Central Tendency & Measures of Variability)

True Score Theory

Empirical observations must have two components (true score & error)

True Score

Something we will never know, not random has patterns

Error

Random, inconsistent has no patterns

Central Tendency

Center of observation , then it must be true

Core / middle

The best representation in central tendency

Mode, Median, & Mean

The three types of center

Mode

Type of center where the frequently occurring value or the value with the highest frequency is considered the true score

Median

Type of center where the physical center is determined as the true score

Mean

This is the gravitational center

Mean

All the weights are taken consideration therefore the values are balanced - this is the true score, the average of the data set

Empirical

Something actually observed

Theoretical

Assumed, or based from theory

Sample

Combination of individuals with common characteristics and demographic statistics

Demographic Statistics

Where they people in a sample are the same ; or the thing they have in common

Total

Combination of individual scores

Typicality

This is introduced when we use average

Variability

Spread, disposition, idea of how different the empirical observations from the true score

Variability

Also knows as measures of error

Deviation from the mean

The extent of how different is the empirical observations from the center , this is the error

Discrepancy

Lacking

Squared deviation from the mean

The amount of how different is the empirical observations from the center , this is the error

Sum of squares

Summation of the squared deviation of the mean ; the total amount of errors ; to visualize how large the data set is

Average squared error

Average amount of deviation from the center

Standard Deviation

The average extent of deviation from the center

Variance

a measure of dispersion that takes into account the spread of all data points in a data set

Object

Forms the sample

Property

Psychological aspect that you observe

Attributes

Set of empirical attributes / attributes you actually observe

Standard Deviation

Represents inconsistency

Sample size, mean & standard deviation

Three things to remember when reporting

Z-score

Ratio of how many times the empirical is to the theoretical

Z-score

How many standard unit score (x) is from the mean

Standard deviation

It is the expected deviation

Mean

This is the observed deviation

Empirical deviation from the mean

Score (x) in relation to the expected score M (mean)

Empirical standardized score

Score X in relation to the expected extent of deviation. From the mean

Variance

Theoretical squared dev from the mean

Skewness

Average symmetry

Kurtosis

Average peakedness

Mean

Average score

Standard deviation

Average extent of dev from the ave score

Variance

Average amount of deviation from the average score

Normality

Symmetry + Peakedness