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# Comparison of Means (t-test)

Summary

A standard score is a common unit of measurement which allows OnTarget to compare variables that measure scores from different scales; however, it does not account for the variance within and between groups. The most commonly used tool in statistical analysis is the difference test. OnTarget has developed several reports that utilize One- and Two-Sample difference tests which allow for the statistical determination of student growth which do account for the variances between and within groups.

The Comparison on Means – Group to State (or single sample t-test) allows districts to determine if the average raw score in their sample is statistically significantly different from the mean raw score of the entire population of students. This analysis could be conducted using
STAAR results at the district, campus, grade, or teacher level. This calculation can be conducted using STAAR results from one year to another.

The Comparison on Means – Year to Year (Same Students Over Time or paired-sample t-test), allows for student growth to be calculated over time. This calculation can be conducted using STAAR results from one year to another, or can also be calculated from district-created benchmarks or common assessments (only after a validity and reliability analysis has been conducted).

The Comparison on Means – Two Different Groups (Independent Sample t-test), allows districts to determine if the average raw score in a group’s sample is statistically significantly different from the mean raw score of another group’s sample. This analysis can be conducted using STAAR results from two different teachers, or two different campuses overall. It can also be conducted using Common Assessment Analysis results.

Usage

• Descriptive Statistics
• General Sample Statistics
• The Normal Curve
• Correlation
• Test Statistics
• Effect Size

Definitions

• Average Raw Score: Calculated by summing all raw score values and dividing by the number of total cases.
• Mean: The average calculated by summing all the values in a data set and dividing by the number of cases.
• Standard Score: A raw score expressed in terms of how many standard deviations it falls away from the mean (also known as z-score).
• Standard Deviation: Tells the average distance by which average scores deviate from the mean.
• Standard Deviation of Average Growth of Students: The average distance by which the average student growth deviates from the mean.
• Standard Error of the Mean: Standard deviation of the sampling distribution of the mean. It tells how much variability there is between each sample mean.
• Sampling Distribution of the Mean: Distribution that shows what the sampling distribution would look like if repeated random samples of the population fell within that area.
• Raw Score Distribution (Graph):
• x-axis: All possible raw scores.
• y-axis: Total # of students with that raw score.
• Red plot line: Mean raw score of the group represented.
• Yellow dotted plot lines: (Mean) +/- (Standard Deviation)
• T-Critical Value: A statistical test value that corresponds to a commonly selected alpha value. As you adjust the alpha, the common zone either increases or decreases making it easier to achieve the rare zone.
• T-Value: The calculated test statistic that compares the sample’s mean to the specified value (other sample’s mean) and determines if a statistically significant difference exists between the two.
• General Normal Distribution (Graph):
• Normal Distribution Curve: A specific bell-shaped curve defined by the percentage of cases that fall in the specific areas of the curve.
• x-axis: Sampling Distribution of the Mean, with the common zone and the rare zone marked.
• y-axis:
• Yellow Plot lines: Divide the common zone from the rare zone, and are called T-Critical Value. (Dependent on user selected Significance Level (Alpha)).
• Common Zone: The section in which sample means commonly fall. If the observed sample mean falls in the common zone, there is no significant difference between the samples.
• Rare Zone: The part of the sampling distribution in which it is rare that the sample mean fall. If the observed sample mean falls in the common zone, then an unusual event has happened and there is a significant difference between the samples.
• Effect Size (Cohen’s D/Partial Eta Squared):
• Cohen’s D: A standard score that allows different effect measured by different variables and different studies to be expressed and compared with a common unit of measure.
• A value of 0 means there is no effect.
• As you get farther away from 0 the size of the effect increases.
• Partial Eta Squared:
• Eta squared measures the proportion of the total variance in a dependent variable that is associated with the membership of different groups defined by an independent variable. Partial eta squared is a similar measure in which the effects of other independent variables and interactions are partialled out.
• Eta Squared (R2): Eta squared measures the proportion of the total variance in a dependent variable that is associated with the membership of different groups defined by an independent variable.
• Correlation: Quantifies the degree of the relationship between two variables and takes the form of a straight line. In a perfect relationship all data points fall on a straight line. The closer the value align to 1, the stronger the relationship. The further aligned from 1, the more scattered the relationship.
• Confidence Interval: A range within which it is estimated that a population value falls. Used to determine the impact of the independent variable (campus/teacher) on the dependent variable (students’ raw scores) in the population.
• z-Score: A raw score expressed in terms of how many standard deviations it falls away from the mean (also known as standard score).

Filters

Single-select:

• What are you comparing?
• What two different groups? (Two Different Groups)
• Subject
• Year
• Campus
• Campus/Teacher #2 (Two Different Groups)
• Version
• Language
• Significance Level (Alpha) – Default 95% (.05)
Updated on 06/06/2022

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