Reliability & Validity

# Alternate Forms Reliability – Methods, Examples and Formulas

## Alternate Forms Reliability

Alternate forms reliability is a measure of reliability used in psychometrics to assess the consistency of measurement across different versions or forms of a test or assessment. It is also referred to as parallel forms reliability or equivalent forms reliability.

### Alternate Forms Reliability Methods

There are several methods commonly used to establish alternate forms reliability. These methods involve creating different versions of a test or assessment that are intended to be equivalent in terms of content, difficulty level, and measurement properties. Here are three common approaches:

#### Split-Half Method

In this method, a single test is divided into two halves, typically by splitting the items into two sets. The two halves should be equivalent and representative of the construct being measured. Each half is then administered to the same group of individuals, and the scores from the two halves are compared. Measures of reliability, such as the Spearman-Brown formula or the Kuder-Richardson formula, are used to estimate the correlation between the two halves. This method is commonly used when it is not feasible to create completely independent test forms.

#### Equivalent Form Method

With this method, multiple test forms are created to measure the same construct. Each form contains different items but is designed to be equivalent in terms of content, difficulty, and measurement properties. The different forms are administered to the same group of individuals in a counterbalanced or randomized manner. The scores obtained from the different forms are then correlated to assess the degree of agreement or consistency between them. Statistical techniques like the Pearson correlation coefficient or the intraclass correlation coefficient (ICC) are often employed for this purpose.

#### Test-Retest Method

Although not strictly an alternate forms reliability method, the test-retest method can be used as an approximation when creating different forms is not feasible. In this method, the same test or assessment is administered to the same group of individuals on two separate occasions with a time interval in between. The scores from the two administrations are then compared using correlation techniques to estimate the reliability. While this method does not involve different forms, it assesses the stability of scores over time and can provide an indication of the consistency of measurement.

### Alternate Forms Reliability Formulas

Pearson Correlation Coefficient (r):

The Pearson correlation coefficient is a measure of the linear relationship between two variables. In the context of alternate forms reliability, it can be used to assess the degree of correlation between the scores obtained from different test forms.

The formula for calculating the Pearson correlation coefficient is as follows:

r = (Σ(X1 – X̄1)(X2 – X̄2)) / √[(Σ(X1 – X̄1)²)(Σ(X2 – X̄2)²)]

where

X1 and X2 are the scores from the two different forms of the test, X̄1 and X̄2 are the means of the scores, and Σ represents the summation symbol.

The Pearson correlation coefficient ranges from -1 to +1, where a value close to +1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates a weak or no correlation.

Intraclass Correlation Coefficient (ICC):

The intraclass correlation coefficient is a statistical measure used to estimate the consistency or agreement between different measurements or ratings. In the case of alternate forms reliability, it can be used to assess the agreement between the scores obtained from different test forms.

There are different types of ICC depending on the specific design and assumptions, but the two most commonly used types for alternate forms reliability are ICC(2,1) and ICC(3,1).I

• CC(2,1) is a single-measure consistency ICC that considers the consistency of scores across the two test forms.
• ICC(3,1) is an average-measures consistency ICC that accounts for both the consistency across test forms and the systematic differences between the forms.

The formulas for ICC(2,1) and ICC(3,1) are more complex and involve analysis of variance (ANOVA) calculations. These calculations are typically performed using statistical software.The ICC values range from 0 to 1, with higher values indicating greater agreement or consistency between the test forms.

### Alternate Forms Reliability Examples

Following are two examples that illustrate how alternate forms reliability can be assessed:

Example 1: Educational Assessment

Let’s say a group of researchers wants to develop an alternate forms reliability study for a mathematics assessment for high school students. They create two different forms of the test, Form A and Form B, with equivalent content and difficulty. Both forms consist of multiple-choice questions.

The researchers administer Form A to a sample of 100 students and record their scores. After a week, they administer Form B to the same group of 100 students. The scores obtained from Form B are then compared to the scores from Form A to assess the alternate forms reliability.

They calculate the Pearson correlation coefficient between the scores of Form A and Form B using the formula I mentioned earlier. The obtained correlation coefficient is 0.85, indicating a strong positive correlation between the two forms. This suggests that the two forms of the test are reliable and produce consistent scores.

Example 2: Personality Inventory

Suppose a psychologist wants to examine the alternate forms reliability of a personality inventory questionnaire. Two different versions of the questionnaire, Version 1 and Version 2, are created. Each version consists of the same set of personality trait items but in a different order.

The psychologist administers Version 1 to a group of 50 participants and records their responses. After a two-week interval, the same participants are given Version 2 of the questionnaire. The scores obtained from Version 1 and Version 2 are then compared to assess the alternate forms reliability.

Using the intraclass correlation coefficient (ICC) formula, specifically ICC(2,1) or ICC(3,1), the psychologist calculates the agreement between the scores obtained from the two versions. The resulting ICC value is 0.92, indicating high agreement between the scores. This suggests that the two versions of the personality inventory are reliable and produce consistent results.

### When to Use Alternate Forms Reliability

Alternate forms reliability is typically used in situations where researchers or test developers want to assess the consistency of measurement across different versions or forms of a test or assessment. Here are some scenarios where alternate forms reliability is particularly useful:

• Minimizing Practice Effects: If the same form of a test is administered multiple times to the same individuals, practice effects can occur, leading to inflated scores on subsequent administrations. By using alternate forms, individuals are exposed to different sets of items, reducing the influence of practice effects and providing a more accurate measure of the construct of interest.
• Reducing Fatigue or Boredom: Administering a lengthy test or assessment can lead to fatigue or boredom, which can negatively impact test performance. By using different forms, individuals are engaged with new items and content, minimizing the effects of fatigue or boredom and maintaining their motivation throughout the assessment.
• Controlling for Memory Effects: Some tests rely on individuals’ memory, such as recall or recognition tasks. If the same items or stimuli are used across multiple administrations, individuals may remember their responses or the correct answers from previous administrations, compromising the validity of the test. Alternate forms help control for memory effects by presenting new items or stimuli, ensuring that individuals respond based on their current knowledge or abilities.
• Counterbalancing Order Effects: In cases where the order of test administration may influence performance, alternate forms can be used to counterbalance the order. For example, if there is a concern that individuals may perform differently based on whether they start with Form A or Form B, using alternate forms allows half of the individuals to start with Form A and the other half to start with Form B, balancing any potential order effects.
• Validation and Cross-validation: Alternate forms reliability is valuable when researchers want to validate a new version or adaptation of an existing test. By comparing the scores obtained from the new form to those obtained from an established form, researchers can assess the degree of consistency between the two forms and evaluate the validity of the new version.

### Applications of Alternate Forms Reliability

Alternate forms reliability has various applications in research, educational settings, and clinical assessments. Here are some common applications of alternate forms reliability:

Test Development:

Alternate forms reliability is often employed during the development of new tests or assessments. Researchers create different versions or forms of the test to ensure that the items are functioning consistently and measuring the intended construct reliably. By establishing alternate forms reliability, researchers can select the most effective and reliable items for the final test form.

Educational Assessments:

Alternate forms reliability is used in educational settings to evaluate the consistency of measurement across different versions of standardized tests. For example, in large-scale assessments such as state exams or college entrance exams, multiple versions of the test may be administered to different groups of students to minimize the impact of cheating and enhance the fairness of the assessment.

Clinical Assessments:

In clinical and psychological assessments, alternate forms reliability can be valuable. Psychologists or clinicians may use different versions of a questionnaire or test to assess various aspects of an individual’s condition or progress over time. By establishing alternate forms reliability, practitioners can ensure that the different forms yield consistent results and accurately measure the targeted constructs.

Research Studies:

Alternate forms reliability is commonly employed in research studies to assess the consistency of measurement across different measurement points. By using different forms of an instrument at different time points, researchers can control for factors such as practice effects, memory effects, or fatigue, and obtain reliable and unbiased data over the course of the study.

Cross-cultural Studies:

Alternate forms reliability can be useful in cross-cultural research where assessments need to be adapted or translated into different languages or cultural contexts. By developing and validating equivalent forms of the assessment in different languages or cultures, researchers can compare scores across different populations and ensure that the measurement remains consistent and valid.

### Limitations of Alternate Forms Reliability

Here are some limitations to consider:

• Development Challenges: Creating multiple equivalent forms of a test can be time-consuming and resource-intensive. Ensuring that the forms have comparable content, difficulty, and measurement properties requires careful planning, item selection, and pilot testing. The process of developing and validating alternate forms can be complex, especially for tests that measure complex constructs.
• Limited Generalizability: Alternate forms reliability estimates are specific to the forms used in the study. The reliability obtained from a specific pair of alternate forms may not necessarily generalize to other versions or forms of the test. Generalizing alternate forms reliability to different contexts, populations, or versions requires additional evidence and validation studies.
• Limited Item Sampling: Each form of the test represents only a subset of the total item pool. As a result, alternate forms reliability may not fully capture the reliability of the complete set of items. Some items may perform differently or have different psychometric properties in different forms, leading to variations in reliability estimates across forms.
• Contextual Variability: The context or testing conditions in which alternate forms are administered can impact performance and reliability. Factors such as time of day, test administration environment, or the presence of different test administrators can introduce variability that affects the reliability estimates. Controlling for these contextual factors can be challenging and may limit the generalizability of the reliability estimates.
• Limited Stability Over Time: Alternate forms reliability estimates assess the consistency of measurement at a specific point in time. However, the equivalence of the forms may change over time due to various factors, such as changes in item difficulty or changes in the construct being measured. Alternate forms reliability should be reassessed periodically to ensure the continued reliability of the test over time.
• Limited Insight into Item Performance: While alternate forms reliability provides an overall estimate of the consistency of measurement across forms, it does not provide detailed information about the performance of individual test items. Assessing item properties, such as item difficulty, discrimination, or item-total correlations, requires separate analyses and is not directly captured by alternate forms of reliability.
• Also see reliability