Chap 3 - Psych Assessment

• • The arithmetic mean, denoted by the symbol X¯ (and pronounced “X bar”), is equal to the sum of the observations (or test scores, in this case) divided by the number of observations. Symbolically written, the formula for the arithmetic mean is X¯ = Σ(X/n)
• • In a bar graph, numbers indicative of frequency also appear on the Y-axis, and reference to some categorization
• • a bimodal distribution because there are two scores (51 and 66) that occur with the highest frequency (of two).
• • coefficient of correlation is the numerical index that expresses this relationship: It tells us the extent to which X and Y are “co-related.”
• • The value obtained for the coefficient of correlation can be further interpreted by deriving from it what is called a coefficient of determination, or r^2 . 
• • The coefficient of determination is an indication of how much variance is shared by the X- and the Y-variables.
• In a continuous scale, the values can be any real number in the scale’s sample space.
• correlation is an expression of the degree and direction of correspondence between two things.
• • A coefficient of correlation (r) expresses a linear relationship between two (and only two) variables, usually continuous in nature.
• Scatterplots are useful in revealing the presence of curvilinearity in a relationship. As you may have guessed, curvilinearity in this context refers to an “eyeball gauge” of how curved a graph is
• • distribution may be defined as a set of test scores arrayed for recording or study.
• • A discrete scale has a sample space that can be counted. 
• • error refers to the collective influence of all of the factors on a test score or measurement beyond those specifically measured by the test or measurement.
• In a frequency distribution, all scores are listed alongside the number of times each score occurred. The scores might be listed in tabular or graphic form.
• • Data illustrated in a frequency polygon are expressed by a continuous line connecting the points where test scores or class intervals (as indicated on the X-axis) meet frequencies (as indicated on the Y-axis).
• • A graph is a diagram or chart composed of lines, points, bars, or other symbols that describe and illustrate data
• • In a grouped frequency distribution, test-score intervals, also called class intervals, replace the actual test scores
• • A histogram is a graph with vertical lines drawn at the true limits of each test score (or class interval), forming a series of contiguous rectangles.
• • The interquartile range is a measure of variability equal to the difference between Q3 and Q1.
• interval scales have meaningful distances between numbers. Each unit on the scale is exactly equal to any other unit on the scale.
• • interval scales contain no absolute zero point. An absolute zero indicates the absence of a quantity. Temperature is usually measured as an interval scale
• • The term testing professionals use to refer to the steepness of a distribution in its center is kurtosis. 
• • Distributions are generally described as platykurtic (relatively flat), leptokurtic (relatively peaked), or—somewhere in the middle— mesokurtic linear transformation
• • the most commonly used measure of central tendency is the arithmetic mean (or, more simply, mean), which is referred to in everyday language as the “average.”
• • measurement as the act of assigning numbers or symbols to characteristics of things (people, events, whatever) according to rules
• • A standard score obtained by a linear transformation is one that retains a direct numerical relationship to the original raw score.
• A nonlinear transformation may be required when the data under consideration are not normally distributed yet comparisons with normal distributions need to be made.
• • A measure of central tendency is a statistic that indicates the average or midmost score between the extreme scores in a distribution.
• • Another tool that could be used to describe the amount of variability in a distribution is the mean absolute deviation, or MAD for short.
• • The median, defined as the middle score in a distribution, is another commonly used measure of central tendency
• Meta-analysis may be defined as a family of techniques used to statistically combine information across studies to produce single estimates of the data under study. The estimates derived, referred to as effect size, may take several different forms. In most meta-analytic studies, effect size is typically expressed as a correlation coefficient.
• • A distribution has a negative skew when relatively few of the scores fall at the low end of the distribution.
• • The most frequently occurring score in a distribution of scores is the mode.
• Nominal scales are the simplest form of measurement. These scales involve classification or categorization based on one or more distinguishing characteristics
• • Theoretically, the normal curve is a bell-shaped, smooth, mathematically defined curve that is highest at its center. 
• • normalizing a distribution involves “stretching” the skewed curve into the shape of a normal curve and creating a corresponding scale of standard scores, a scale that is technically referred to as a normalized standard score scale
• • ordinal scales assign people to categories. Unlike nominal scales, ordinal scales have categories with a clear and uncontroversial order. 
• • An outlier is an extremely atypical point located at a relatively long distance—an outlying distance—from the rest of the coordinate points in a scatterplot
• a positive skew when relatively few of the scores fall at the high end of the distribution.
• • The range of a distribution is equal to the difference between the highest and the lowest scores.