psychological statistics

original, unchanged scores that are the direct result of measurement

purpose is to identify and describe the exact location of every score in the distribution. to standardize an entire distribution. (IQ scores)

X-M. measures the distance in points between X and M and indicates whether X is located above or below the mean.

transforming all of the x scores to z-scores. shape of distribution will always be same as x scores. mean of z-scores will always be zero. distribution of z-scores will always have a standard deviation of 1.

composed of scores that ahve been transformed to create predetermined values for Mu or Sigma. Standardized distributions are used to make dissimilar distributions comparable.

ask Gurtman

For a situation in which several different outcomes are possible, the probability for any specific outcomes is defined as a fraction or a proportion of all the possible outcomes. If the possible oucomes are identified as A, B, C, D and so on, then probability of A = # of outcomes classified as A / total # of possible outcomes

requires that each individual in the population has an equal chance of being selected. A second requirement, necessary for many statistical formulas, states that the probabilities must stay constant from one selection to the next if more than one individual is selected.

to keep the probabilities from changing from one selection to the next, it is necessary to return each individual to the population before you make the next selection.

a complete listing of z-scores and proportions is provided. Lists proportions of the normal distribution for a full range of possible z-score values.

the percentage of the individuals in the distribution who have scores that are less than or equal to the specific score.

when a score is referred to by its percentile rank, the score is called a percentile. (i.e., a score with a percentile rank of 70% is called the 70th percentile)

the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter

the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.

a distribution of statistics obtained by selecting all the possible samples of a specific size from a population

For any population with mean M and standard deviation s, the distribution of sample means for sample size n will have a mean of M and a standard deviatioin of s divided by square root of n and will approach a normal distribution as n approaches infinity

The mean of the distribution of sample means is equal to the mean of the population of scores, M.

The standard deviation of the distribution of sample means sigma sub M, is called the standard error of M. The standard error provides a measure of how much distance is expected on average between a sample mean (M) and the population mean (m).

the larger the sample size (n), the more probable it is that the sample mean will be close the population mean.

refers to methods for organizing, summarizing and interpreting data

the entire set of individuals one wishes to study.

a group selected from a population, usually for the purposes of research

a characteristic or condition that changes or has different values for different individuals

measurements or observations

a collection of measurements or observations

a single measurement or observation

a single measurement or observation. Also called datum

a value, usually numerical, that describes a population. Usually derived from measurements of individuals in the population.

a value, usually numerical, that describes a sample. Usually derived from measurements of the individuals in the sample.

statistical procedures used to summarize, organize, and simplify data.

techniques that allow us to study samples and then make generalizations about the populations from which they were selected

the discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter

two different variables are observed to determine whether there is a relationship between them.

involves comparing groups of scores. Also called experimental research strategy. The goal of experimental study is to demonstrate a cause and effect relationship between two variables. Specifically the experiment attempts to show that changing the value of one variable causes changes to occur in the second variable. Involves manipulation & control.

the variable that is manipulated by the researcher. Usually consists of two or more treatment conditions to which subjects are exposed. The independent variable consists of the antecedent conditions that were manipulated prior to observing the dependent variable.

is the one that is observed to assess the effect of treatment

individuals in the control condition do not receive the experimental treatment. Instead, they either receive no treatment or they receive a neutral, placebo treatment. The purpose of a control condition is to provide a baseline for comparison with the experimental condition.

Individuals in the experimental condition do receive the experimental treatment

involves comparing two groups of scores, however, the researcher has no ability to control which particpants go into which group.(i.e., comparing 8 y/o boys to 10 y/o boys; individuals with/out an eating disorder; children from single/two parent homes. It is impossible to use random assignment to control participant variables and ensure equivalent groups. NOT a true Experiment.

involves comparing two groups of scores, however the researcher has no control over the passage of time. Difference may be caused by treatment or just change as time goes by. Researcher has no control over other variables that change with time. NOT a true Experiment.

in a nonexperimental study, the "independent variable" that is used to create the different groups of scores is often called the quasi-independent variable. (i.e., gender is not a true independent variable because it is not manipulated)

internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior (IQ, anxiety, hunger)

identifieds a measurement procedure (a set of operations) fore measuring external behavior and uses the resulting measurements as a definition and a measurement of a hypothetical construct. Note that an operational definition has two components. First, it describes a set of operations for measuring a construct. Second it defines the construct in terms of the resulting measurements. (i.e., performance on an IQ test measures intelligence, hours since last meal measures hunger)

consists of separate, indivisible categories. No values can exist between two neighboring categories. (dice, number of children)

there are an infinite number of possible values that fall between any two observed values. A continuous variable is divisible into an infinite number of fractional parts.

the boundaries of intervals for scores that are represented on a continous number line. The real limit separating two adjacent scores is located exactly halfway between the scores. Each score has two real limits (upper and lower).

is at the top of the interval

at the bottom of the interval

consists of a set of categories that have different names. Measurements on a nominal scale label and categorize observations, but do not make any quantitative distinctions between observations.

consists of a set of categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size or magnitude. (i.e., small, med, lg)

consists of ordered categories that are all intervals of exactly the same size. Equal differences between numbers on scale reflect equal differences in magnitude. However, the zero point on an interval scale is arbitrary and does not indicate a zero amount of the variable being measured.

is an interval scale with the additonal feature of an absolute zero point. With a ratio scale, ratios of numbers do reflect ratios of magnitude.

an organized tabulation of th enumber of individuals located in each category on the scale of measurement.

from the lowest score to the highest score

grouping scores into intervals and then listing the intervals in the table instead of listing each individual score.

groups of scores used in a grouped frequency distribution

the concept of real limits applied to class intervals of a grouped frequency distribution table.

used to display a distribution for interval or ratio scales. A bar is drawn above each score so that the height of the bar corresponds ot the frequency. Each bar extends to the real limits of the score, so that the adjacent bars touch.

graph used to display a distribution for interval or ratio scales. A dot is placed above the midpoint of each score or class interval so that the geight of the dot corresponds to the frequency; then lines are drawn to connect the dots.

graph used to display distribution for nominal or ordinal scales. Bar graphs are similar to histograms except that gaps are left between adjacent bars.

graph that can show the relative (not absolute) number of bluegill and bass in a lake

it is possible to draw a vertical line through the middle so that one side of the distribution is a mirror image of the other

the scores tend to pile up toward one end of the scale and taper of gradually at the other end

the section where the scores taper off toward one end of a distribution

a skewed distribution with the tail on the right-hand side is said to be positively skewed. because the tail points toward the positive (above-zero) end of the X-axis.

a skewed distribution with the tail on the left-hand side because the tail points toward the negative (below-zero) end of the X-axis.

a statistical measure to determine the single score that defines the center of a distribution. The goal of central tendency is to find the single score that is most typical or most representative of the entire group.

• m=(SX)/N
• sum of scores divided by the number of scores

• M=(SX)/n
• our own alphabet for samples

weighted mean = (combined sum/combined n)=(Sum(X1) + Sum(X2))/n1 +n2

if the score sin a distribution are listed in order from smallest to largest, the median is the midpoint of the list

in a frequency distribution, the mode is the score or category that thas the greatest frequency

a distribution with two modes

a distribution with more than two modes

when two modes have unequal frequencies, researchers occasionally differentiate the two values by calling the taller peak the major mode

when two modes have unequal frequencies, researchers occasionally differentiate the two values by calling the shorter peak the minor mode

graph used when the values on the horizontal axis are measured on an interval or ratio scale. A point is placed above each treatment condition. The points are connected with straight lines.

the right side of the graphi sa mirror image of the left side. The median is exactly at the center. The mean is exactly at the center. Mean=median If only one mode, the mode will be at the center. Mean=median=mode.

in skewed distributions, the mode is located toward the side where the scores pile up, and the mean is pulled toward the extreme scores in the tail. The median is usually located between these two values.

mode, median, mean

mean, median, mode

provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. Defined in terms of distance.

the distance covered by the scores in a distribution, from the smallest score to the largest score

• deviation is the distance from the mean
• deviation score = X-m

equals the mean squared deviation. Variance is the average squared distance from the mean

our goal is to measure the standard distance from the mean. Standard deviation is the square root of the variance.

• is the sum of the squared deviation scores
• SS=Sum (X-m)squared

sample variance = s squared = sum of squares divided by n-1

sample standard deviation = s = square root of s squared = square root of sum of squares divided by n-1

For a sample of n scores, the degrees of freedom, or df, for the sample variance are defined as df=n-1. The degrees of freedom determine the number of scores in the sample that are independent and free to vary.

a sample statistic is biased if the average value of the statistic either underestimats or overestimates the corresponding population parameter.

a sample statistic is unbiased if the average vale of the statistic is equal to the population parameter. (The average value of the statistic is obtained from all the possible samples for a specific sample size, n)