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Population is described by a parameter that is represent all the individuals that a researcher is seeking to study.
Sample a statistic of a population that represents a smaller portion of the population.
Sampling Error is described by the discrepancy between a parameter and a statistic.
Dependent variable is the variable that changes within a study.
Independent variable is manipulated by the researcher but remains the same throughout the study.
Population vs Sample: There are two different data samples that must be distinguished to gain a reliable understanding of the population and sample within variance and standard deviation. Population is a representation of the total of individual studied and sample is just a portion of the population.

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The degree to which a certain inference from a test is appropriate or meaningful. There are two different methods of referencing validity, the method that is focused on in this course is an assessment or the method data is collected. When validating an assessment, several types of evidence are needed and although evidence will vary the most substantial evidence will be a single line of solid evidence. The resources that are used for evidence are a reflection of the value of the test.
Various Types of Validity:

Criterion: Supports a proposed construct interpretation of scores on a test based on theoretical implications associated with the construct label.

Content: Establishes what the test includes within its domain and excludes content outside the domain.

Construct: The extent to which scores on a test are related to a criterion measure.

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How consistent performance on a test is amongst a variety of conditions. Inferences are justified based on test scores it's not a property of the test but of the inferences that can be made from the test score. The theory of reliability is directly associated with the true score theory, which can involve either random error (single tester) and systematic error (all testers). There are different ways that reliability can affect the results in a test, for this reason, there are different types of reliability: Inter-rater or inter-observer, test-retest, parallel forms, internal consistency.
Interrater Reliability: This term can also be known as inter-observer reliability. It estimates reliability based on how all observers/raters give a consistent estimate to the same observation. We want every observer to agree on a rate of at least 85% to have witnessed an object/phenomenon.

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When applying formative assessments into practice the first thing that an educator must consider if what they want to gain from the assessment. Are they seeking to gain an understanding of how students compare to one another or are they seeking to help a student by gaining information about their performance and using to enhance the lesson material? This distinguishes the difference between assessment for learning or assessment of learning.

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Mean represents the average of numbers in a sample of data. There are two types, population sample: μ, and the sample mean: x̅.
Median is the midpoint within a sorted list of numbers in a sample of data.
Mode is the number within a sample of data that appears the most in a sample.
Variance describes how far the distribution of numbers is between the lowest/highest number in a sample from the mean. The symbol for variance can be represented by : σ2
The symbol for sample variance can be represent by: s 2
Standard Deviation represents a measure of how spread out numbers will be in distribution.
The symbol for standard deviation is: σ
The symbol for the standard deviation sample is: SD or s

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Can be used interchangeably with latent trait models. Through IRT, the assessment is being measured at the item level and can be manipulated for use in several different ways. IRT allows for item banking, which means individuals can be provided with different items within an assessment and still be evaluated in the same content. Also, IRT creates the opportunity to modify a test based on the individual who is taking the test.

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Item analyses provides a way to measure the quality of answer choices and reusing questions based on knowledge gained from previous test performance, i.e. test bank; it does so through two measures: difficulty index and discrimination index.
Difficulty index is used to determine the difficulty level on an array of items on an assessment. For example, analyzing how difficult assessment options are on a multiple choice quiz through recording how many responses were received for each answer choice. Discrimination index analyzes how well high performers make answer choices compared to low performers. There are two different types, positive and negative discrimination index. Positive associates to how well high performers make correct answer choices compared to low performers. On the other hand, negative relates to how often low performers choose the correct answer choice.

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Consistency of Measurement (Reliability): the consistency in which a test form is measuring an underlying construct. The construct is characterized by a trait, ability, or behavior that a student may exhibit during a test. In order for a test to be deemed reliable, it must have an index score of .8.
Consistency of Ratings (Validity): the consistency in test scores and what inferences can be made based on the consistency of those ratings. High values in ratings are considered valuable and a value above .7 is considered excellent.

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Is used to measure reliability on an assessment as a whole. With the analysis of the assessment, random error can be factored out of the results of the test to better understand how the tester performed without any extraneous factors, or random errors. The statistics for CTT are generalized to understand the students that are taking a specific test and the quality of question difficulty level. Furthermore, it uses a true score to test the reliability measured, i.e. X = T + E. X is the true score, T is the observed score, and E represents the errors in the test.

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We must understand the different types of test and the way the statistics can be applied amongst those test. These differences can be seen in the way that some test score compared to others. For example, a standardized test will gain a standard score of a students performance compared to others while age equivalent score test will see growth in a child through age. Some ways of distinguishing various test from one another are through understanding the norms (national, local, age, grade) amongst test. Test that can be used to interpret a variety of things about a student but ultimately they should be used for the benefit of the student, i.e. assessment for learning. However, that is not always the case when you're seeking to compare students to one another through the use of assessment.

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Measurement: the assignment of values within a system according to rules.
Measurement Rules:

There must be an absence of bias.

Must be based on a clearly articulated goal, what will be measured, for whom and why.

The basic need for measurement is represented by the object, variable, and values/units.

Measurement Scales:

Nominal: consist of categories with no numeric scales, for example, males/females, extroverts/introverts, republican/democrat.

Ordinal: is used to describe variables that can be ranked in order, for example, economic status or ranking.

Interval: an ordinal series of categories that are within equal-sized units for example temperature.

Ratio: an interval scare with an absolute/true zero point and cannot be negative for example weight, income. Statistical based use.

Scoring: There is a variety of scale scores that are used to determine the value of the results in different types of assessment. Understanding how to interpret the scoring on different test forms will create an opportunity to educate those that you work with and speak more intelligently on the subject. Some examples of different types of scale scores are raw scale score, percentage-mastery scale, age equivalent, grade equivalent, IQ, and percentile rank scale.