Reliability & Validity

# Split-Half Reliability – Methods, Examples and Formulas

## Split-Half Reliability

Split-half reliability is a measure used to assess the internal consistency or reliability of a psychometric test or measurement instrument. It is commonly used in fields such as psychology, education, and social sciences to evaluate the consistency of test items or scale scores.

In split-half reliability, the test or measurement instrument is divided into two halves or subsets of items, and the scores on each half are compared. The division of items can be done in various ways, such as odd-even split (e.g., comparing the scores of odd-numbered items with even-numbered items) or random split (e.g., randomly assigning items to two halves).

The split-half reliability coefficient is then calculated to determine the consistency of scores between the two halves. The most common coefficient used is the Pearson correlation coefficient, which ranges from -1 to +1. A higher correlation coefficient indicates greater internal consistency or reliability.

To calculate the split-half reliability coefficient, the following steps are typically followed:

• Divide the items of the test into two equal halves or subsets.
• Calculate the scores for each half by summing the item scores.
• Calculate the correlation coefficient (e.g., Pearson correlation) between the scores of the two halves.
• Apply a reliability estimation method, such as the Spearman-Brown prophecy formula or the corrected split-half coefficient formula, to adjust the coefficient to the full-length test.

### Split-Half Reliability Methods

There are several different approaches to split-half reliability, including:

#### Odd-Even Split

In this method, the items with odd numbers are grouped together as one half, and the items with even numbers are grouped together as the other half. The responses on each half are then compared to determine the reliability. This method assumes that there is no systematic difference between the odd and even items.

#### Parallel Forms Split

This approach involves creating two parallel forms of the measurement scale, where each form contains the same number of items that assess the same construct. The two forms are administered to the same group of participants, and the responses on each form are compared to estimate the reliability. This method is useful when it is difficult to split the items into two comparable halves.

#### Random Split

In this method, the items are randomly divided into two halves. The responses on each half are then compared to assess the reliability. Random splitting is often used when the scale has a large number of items and the odd-even or parallel forms split is not feasible or practical.

#### Spearman-Brown Prophecy Formula

The Spearman-Brown formula is used to estimate the reliability of a full-length scale based on the reliability of a shorter version of the scale. It can be applied when the scale is divided into two halves and the split-half reliability coefficient is known. The formula allows researchers to estimate the reliability of the full-length scale if the number of items is increased or decreased.

### Split-Half Reliability Formulas

Split-half reliability is typically calculated using various formulas that assess the degree of correlation between the scores obtained from the two halves of the measurement scale. There are a few common formulas used to calculate split-half reliability:

Pearson Product-Moment Correlation:

This formula calculates the Pearson correlation coefficient between the scores on the two halves of the scale. It measures the linear relationship between the two sets of scores and ranges from -1 to +1.

The formula is as follows:

Split-half reliability coefficient = 2 * (r / (1 + r))

where

“r” represents the Pearson correlation coefficient between the scores on the two halves of the scale.

……………………

Spearman-Brown Prophecy Formula:

This formula is used to estimate the reliability of a full-length scale based on the reliability of a shorter version of the scale. It is commonly applied when the scale is divided into two halves, and the split-half reliability coefficient is known.

The formula is as follows:

Split-half reliability coefficient (full scale) = (2 * Split-half reliability coefficient) / (1 + Split-half reliability coefficient)

where

“Split-half reliability coefficient” represents the reliability coefficient obtained from the split-half analysis.

………………………

Guttman Split-Half Formula:

The Guttman formula is an alternative method to estimate the split-half reliability coefficient. It uses the Spearman-Brown formula and is based on the length of the scale.

The formula is as follows:

Split-half reliability coefficient = (2 * Spearman-Brown coefficient) / (1 + (Spearman-Brown coefficient * (k – 1)))

where

“Spearman-Brown coefficient” represents the reliability coefficient obtained from the Spearman-Brown prophecy formula, and “k” represents the length of the full-length scale.

### Split-Half Reliability Examples

Split-Half Reliability Examples are as follows:

Example 1:

Suppose you have a questionnaire with 10 items measuring self-esteem. You administer the questionnaire to a sample of 100 participants, and you want to assess the split-half reliability of the scale.

Step 1: Divide the items into two halves. Let’s randomly assign items 1, 3, 5, 7, and 9 to the first half (odd items), and items 2, 4, 6, 8, and 10 to the second half (even items).

Step 2: Calculate the total score for each participant on each half of the scale.

Step 3: Compute the correlation coefficient between the scores obtained on the two halves using the Pearson product-moment correlation formula:

Split-half reliability coefficient = 2 * (r / (1 + r))

Let’s assume the correlation coefficient (r) between the two halves is 0.80.

Split-half reliability coefficient = 2 * (0.80 / (1 + 0.80)) = 2 * (0.80 / 1.80) = 0.89

The split-half reliability coefficient for the self-esteem scale is 0.89.

…………………

Example 2:

Consider a multiple-choice exam with 50 items assessing knowledge of biology. You want to estimate the split-half reliability of the exam.

Step 1: Randomly divide the items into two halves, creating Form A and Form B of the exam.

Step 2: Administer both Form A and Form B to a sample of 200 students and obtain their scores.

Step 3: Calculate the correlation coefficient between the scores on Form A and Form B using the Pearson product-moment correlation.

Let’s assume the correlation coefficient (r) between the two forms is 0.85.

Split-half reliability coefficient = 2 * (r / (1 + r)) = 2 * (0.85 / (1 + 0.85)) = 0.94

The split-half reliability coefficient for the biology exam is 0.94.

### When to use Split-Half Reliability

Split-half reliability is commonly used in research and assessment contexts to assess the internal consistency or reliability of a measurement scale. It is particularly useful in situations where the scale consists of multiple items or questions that are intended to measure the same construct.

Here are some scenarios where split-half reliability is appropriate:

Questionnaires or Surveys:

If you have a questionnaire or survey with multiple items that assess the same construct, you can use split-half reliability to evaluate the consistency of responses across the items. This is helpful in determining if the items are measuring the construct reliably.

Psychological Tests:

In psychological testing, split-half reliability can be employed to evaluate the internal consistency of test items. For example, if a personality test consists of several subscales or dimensions, split-half reliability can assess the consistency of responses within each subscale.

Educational Assessments:

When developing or using educational assessments, such as exams or tests, split-half reliability can determine how well the items within the assessment are measuring the same knowledge or skill. It helps evaluate the consistency of student responses on different halves of the assessment.

Research Instruments:

Researchers often use scales or instruments with multiple items to measure variables of interest. Split-half reliability can be applied to assess the consistency of responses across these items, ensuring that the scale provides reliable measurement of the intended construct.

### Applications of Split-Half Reliability

Split-half reliability has several practical applications in research, assessment, and evaluation. Some key applications of split-half reliability include:

Scale Development:

Split-half reliability is commonly used in the early stages of scale development to assess the internal consistency of newly developed scales. Researchers can split the items into two halves and examine the correlation between the scores obtained on each half to determine the reliability of the scale. This helps in identifying problematic items and refining the measurement instrument.

Assessment of Internal Consistency:

Split-half reliability provides a measure of the internal consistency of a measurement scale. By examining the correlation between the scores on two halves of the scale, researchers can assess how consistently the items measure the same construct. This information is valuable in determining the overall reliability and quality of the scale.

Comparative Evaluation of Measurement Tools:

When researchers have multiple measurement tools available to assess the same construct, split-half reliability can be used to compare their internal consistency. By calculating split-half reliability coefficients for each tool and comparing them, researchers can determine which tool demonstrates higher internal consistency and is more reliable for measuring the construct of interest.

Quality Assurance in Assessments:

In educational or employment settings, split-half reliability can be employed to evaluate the consistency and reliability of assessments. For example, if a test or exam is divided into two equivalent halves, the correlation between the scores on each half can indicate the internal consistency of the assessment and provide insights into its overall reliability.

Assessment of Change or Stability:

Split-half reliability can be useful in longitudinal or repeated measures studies to assess the stability or change in participants’ scores over time. By calculating split-half reliability coefficients for different time points, researchers can determine if the scores remain consistent over time or if there are fluctuations in the measurement.

Quality Control in Survey Research:

In large-scale survey research, split-half reliability can be used as a quality control measure to assess the consistency of responses across different halves of the questionnaire. By examining the correlation between the scores on each half, researchers can identify any potential issues with the measurement instrument or response patterns.

### Importance of Split-Half Reliability

Here are some key reasons why split-half reliability is significant:

Assessing Internal Consistency:

Split-half reliability provides a measure of the internal consistency of a measurement scale. It allows researchers and practitioners to determine how consistently the items or questions in a scale measure the same construct. High split-half reliability indicates that the items within the scale are measuring the construct consistently, while low split-half reliability suggests that the items may be measuring different aspects or are not reliable indicators of the construct.

Ensuring Measurement Quality:

Split-half reliability helps in assessing the quality of a measurement scale. A reliable scale produces consistent results, allowing researchers to have confidence in the accuracy and precision of the measurements. By calculating split-half reliability coefficients, researchers can evaluate the reliability of a scale and make informed decisions about its suitability for their research or assessment purposes.

Item Analysis and Scale Refinement:

Split-half reliability analysis provides valuable information about individual items within a scale. By examining the correlations between the responses to different halves of the scale, researchers can identify items that are not consistently measuring the construct or that exhibit weak correlations with other items. This analysis helps in refining the measurement scale by eliminating or modifying problematic items and improving the overall reliability of the scale.

Comparing Measurement Tools:

Split-half reliability allows for the comparison of different measurement tools or scales that assess the same construct. By calculating split-half reliability coefficients for each tool, researchers can determine which tool demonstrates higher internal consistency and is more reliable for measuring the construct of interest. This information aids in the selection of the most appropriate measurement tool for a given research or assessment context.

Validity Assessment:

Split-half reliability is closely linked to the concept of validity, particularly internal consistency validity. When a scale demonstrates high split-half reliability, it suggests that the items within the scale are measuring the same underlying construct and are consistent with each other. This provides evidence for the internal consistency validity of the scale and supports the interpretation and generalization of the scale scores.

Decision Making:

Split-half reliability provides researchers and practitioners with a quantitative index to make informed decisions about the use of a measurement scale. It helps in determining whether the scale is suitable for research purposes, such as group comparisons or tracking changes over time. Additionally, split-half reliability information is relevant for establishing cut-off scores, interpreting scale scores, and making decisions based on the scale results.

### Limitations of Split-Half Reliability

It’s important to be aware of these limitations when interpreting and relying on split-half reliability estimates. Here are some key limitations:

• Limited Assessment of Reliability: Split-half reliability estimates only provide an estimate of the internal consistency of a measurement scale based on the correlation between two halves of the scale. This approach does not capture the full range of sources of measurement error or variability in the data. Other sources of error, such as item-specific error or response bias, are not accounted for in split-half reliability estimation.
• Dependency on Item Composition: The reliability estimate obtained through split-half analysis can vary depending on how the items are split into halves. The composition of the two halves can influence the observed correlation and, subsequently, the reliability coefficient. If the split is not optimal, it can result in an underestimation or overestimation of the true reliability of the scale.
• Susceptibility to Item Order Effects: The order in which items appear in a scale can affect the correlation between the two halves. Split-half reliability assumes that the order of items does not systematically influence responses. However, if there is an order effect or item sequence effect present, it can bias the reliability estimate obtained through split-half analysis.
• Limited Generalizability: Split-half reliability is based on a single division of the items into two halves. The reliability estimate obtained from one split may not be representative of the scale’s reliability in other splits. Different divisions of the items can yield different reliability coefficients. Therefore, the split-half reliability estimate may not generalize well to different samples or contexts.
• Sensitivity to Test Length: Split-half reliability is influenced by the length of the scale. Longer scales tend to have higher split-half reliability coefficients because there are more items contributing to the correlation. Short scales may yield less reliable estimates due to limited item representation. The Spearman-Brown prophecy formula can be used to estimate the reliability of the full-scale based on a split-half estimate, but this assumes that the relationship between length and reliability is linear, which may not always hold.
• Assumption of Equivalent Halves: Split-half reliability assumes that the two halves of the scale are equivalent in terms of item difficulty, item discrimination, and content representation. If the two halves are not comparable, such as having unequal numbers of items or different item characteristics, the reliability estimate may be biased.

Also see Reliability 