Book Psych 10 Terms

Weighted Mean

(Denoted Mw) is the combined means of tow or more groups of scores in which the number of scores in each group is disproportionate or unequal Mw= sum(M*n)/sum(n) or weighted sum / combined n

Nonmodal distribution

(rectangular distribution) Is a distribution of scores where all the scores occur at the same frequency. There is NO mode

Operational Definition

A description of some observable event in terms of the specific process or manner by which it was observed or measured. A description of how the Dependent Variable was measured. ex. exam performance from 0 to 100%

Modal distribution

A distribution of scores in which one or more scores occur most often or most frequently

Unimodal distribution

A distribution of scores in which one score occurs mot often. A unimodal distribution has one mode

Skewed distribution

A distribution of scores that includes outliers or scores that fall substantially above or below most of the other scores in the data set

Multimodal distribution

A distribution that has more than two modes

Ogive

A dot-and-line graph used so summarize the cumulative percent of continuous data at the upper boundary of each interval

Frequency Polygon

A dot-and-line graph used to summarize the frequency of the continuous data at the midpoint of each interval Used to summarize the same types of data as histograms

Histogram

A graphical display used to summarize the frequency of continuous data that are distributed in numeric intervals (grouped) 3 Rules: 1. vertical rectangle represents the frequency for that interval 2. the base of each rectangle begins and ends at the upper and lower boundaries of each interval (should have the same width and cannot be constructed with open intervals) 3. Each rectangle touches the adjacent rectangles - data is measured along a continuum

Sector

A particular portion of a pie chart

Quasi-independent variable

A preexisting variable that is often a characteristic inherent to the individual, which differentiates the groups or conditions being compared in a research study. Because the levels of the variable are preexisting, it is not possible to randomly assign participants to groups. A quasi-experimen is a study that: 1. has a quasi-independent variable 2. lacks a comparison/control group In a quasi-experiment: variables being studied cannot be manipulated - making random assignment impossible ex. sex

Percentile Rank

A score is the percentage of scores with values that fall below a specified score in a distribution

Grouped data

A set of scores distributed into intervals, where the frequency of each score can fall into any given interval

Simple frequency distribution

A summary display for 1. the frequency of each individual score or category in a distribution (ungrouped data) 2. the frequency of scores falling within assigned groups (grouped data)

Normal distribution

A theoretical distribution in which scores are symmetrically distributed above and below the mean, median, and the mode at the center of the distribution Eight Characteristics: 1. Is mathematically defined 2. Theoretical 3. Mean, median, and mode are all located at the 50th percentile 4. Symmetrical 5. Mean can equal any value (+or- infinity) 6. The SD can be any positive value 7. The total are under the curve is 1 8. The tails are asymptotic

Random event

Any event in which the outcome observed can vary

Fixed Event

Any event in which the outcome observed is always the same

Degrees of Freedom (df)

Are the number of scores in a sample that are free to vary. All scores except one are free to vary in a sample: n-1 This term is placed in the denominator of the formula for sample variance

Interval boundaries

Are the upper and lower limits for each interval

Coding

Categorical variables -> converted to numeric values ex. race, sex, nationality, etc. (assigned to be numbers)

Quartiles

Contain 25% of the data

Ordinal Scales

Convey order alone (dont convey differences, just order) ex first, second, last

Chebyshev's Theorem

Defines the percentage of data from any distribution that will be contained within any number of standard deviations (where SD>1)

Cumulative frequency distribution

Describes the sum of scores across each range and always sums to the total number of scores in a distribution

Outliers

Extreme scores hat fall substantially above or below most of the scores in a particular data set

Experiment

Fully controls conditions and experiences of partacipnts by applying three required elements of control: (manipulation, randomization, and comparison/control) to isolate the cause-and-effect relationships between variables **know the three elements - (manipulation, randomization, and comparison/control)

Bimodal distribution

Has two modes

Correlational Method

Involves measuring the relationship between pairs of scores no variable manipulation

Standard normal transformation (z transformation)

Is a formaula used to convert any normal distribution with any mean and any variance to a standard normal distribution with a mean equal to zero and a standard deviation equal to 1 Z = x- mean /SD

Variability

Is a measure of dispersion or spread of scores in a distribution and ranges from zero to positive infinity Measures include: Range, Variance, and Standard Deviation

Semi IQR (SIQR)

Is a measure of half the distance between the upper quartile (Q3) and the lower (Q1) of a data set, and is computed by dividing the IQR in half

Standard Deviation

Is a measure of variability for the average distance that scores deviate from their mean. It is the square root of the variance Characteristics: 1. Always Positive 2. Describes Quantitative data 3. Most informative when reported with the mean 4. the value is affected by each score in the distribution -Adding or subtracting the same constant to each score will not change the distance the score diverts from the mean - therefore, will not change the SD -Multipling or dividing each score using the same constant will cause the SD to change by that constant

Variance

Is a measure of variability for the average squared distance that scores deviate from their mean

Standard Normal Distribution (z distribution)

Is a normal distribution with a mean equal to zero and a SD of 1. Is distributed in z-score units along the x-axis The mean corresponds to a z score of zero

Population

Is a set of all individuals, items, or data of interest. This is the group about which scientists will generalize

Sample

Is a set of individual items, or data, selected from a population of interest

frequency distribution

Is a summary display for a distribution of data organized or summarized in therms of how often a category, score, or range of scores occurs

Unit normal table

Is a type of probability distribution table displaying a list of z scores and the corresponding probabilities (or proportions of area) associated with each z score listed.

Z-score

Is a value on the x-axis of a standard normal distribution. The numerical value of a z score specifies the distance or the number of standard deviations that a value is below or above the mean

Definitional formula for variance

Is a way to calculate the population variance and sample variance that requires summing the squared difference of scores form their mean to compute the SS in the numerator

Computational formula for variance

Is a way to calculate the population variance and sample variance without needing to sum the squared differences of scores from their mean to compute the SS in the numerator

Biased Estimator

Is any sample statistic, such as the sample variance when we divide SS by n, obtained from a randomly selected sample that does not equal the value of its respective population parameter, such as a population mean, on average

Unbiased Estimator

Is any sample statistic, such as the sample variance when we divide SS by n-1, obtained from a randomly selected sample that equals the vale o fits respective population parameter, such as a population variance, on average

Sum of Squares (SS)

Is the sum of the squared deviations of scores from their mean. The SS is the numerator in the variance formula Why square the deviations form the mean? 1. the sun of the differences form the mean is zero 2. the sum of the squared differences of scores from their mean is minimal 3. squaring scores can be corrected by taking the square root

Nominal scale

Measurements in which a number is assigned to represent (identify) something or someone One is not greater than another: it is simply different ex. zip codes, licens plates, SS numbers

Data

Measurements or observations: usually referred to as score or raw score

Interval

Measurements that have no true zero and are distributed in equal units The zero is arbitrary (not meaningful) ex. Rating scale, temperature, etc.

Real range

One more than the difference between the largest and smallest value in a data set

Negative Skew

Outliers are substantially smaller (toward the left tail in a graph)

Inferential statistics

Procedures used that allow researchers to infer or generalize observations make with sales to the larger population from which they were selected

Descriptive statistics

Procedures used to summarize, organize, and make sense of a set of scores or observations. Descriptive statistics are typically presented graphically, in tabular form (in tables), or as summary statistics (single variable)

Random Assignment

Random procedure used to ensure that participants in a study have an equal chance of being assigned to a particular group or condition

Scales for measurement

Rules for how the properties of numbers can change with different uses Nominal Ordinal Interval Scale/ratio

Lower and Upper Boundaries

Smallest and largest value of a frequency distribution

Empirical Rule

States that for data that are normally distributed, at least 99.7% of data lie within three standard deviations of the mean, at least 95% of data lie within two standard deviations of the mean, and at least 68% of data lie within one SD of the mean.

Central Tendency

Statistical Measures for locating a single score that is most representative or descriptive of all scores in a distribution

Mean

Sum of a set of scores in a distribution, divided by the total number of summed scores also the "average" and balance point of a distribution. Its value shifts in a direction that balances sets of scores The difference of each score from the mean always sums to zero Summing the squared differences of each score from its mean produces a minimal solution. If you replace the mean with any other value, the solution will be larger Typically used to describe interval and ration scale data that are normally distributed

Cumulative relative frequency/percent distribution

Summary display that distributes the sum of relative frequencies across a series of intervals (bottom up). Sum to 1.0 or 100% respectively

Sample Space

The Total number of possible outcomes that can occur within a given random event

Population variance

The average squared distance that scores in a population deviate from the mean. It is computed only when the scores of a given population are recorded Divide the SS by N

Sample variance

The average squared distance that scores in a population deviate from the mean. It is computed only when the scores of a given sample are recorded Divide the SS by one less than the sample size (n-1) (n-1) is an unbiased estimator

Range

The difference between the largest and smallest value in a data set Only consider the largest and smaller value different than the "real range" (range +1) - which is used for continuous data

Deviation

The difference of each score from its mean

Probability

The frequency of times an outcome occurs divided by the total number of possible outcomes - allows us to make predictions regarding random events - is a measure for the likelihood of observing an outcome in a random event p(x)= f(x)/ sample space (ex 1/2 for flipping a coin) Characteristics: 1. Between 0 and 1 2. Can never be negative

Sample Size

The number of individuals who constitute a subset of those selected from a larger population. Represented by: n

Positive Skew

The outliers are substantially larger (towards the right tail in a graph)

Science

The study of phenomena, such as behavior, through strict obsevation, evaluation, interpretation, and theoretical explanation.

Mode

The value in a data set that occurs most often

Independent Variable

The variable that is manipulated in the experiment. It is the "presumed cause."

Dependent Variabel

The variable that is measured in each group of a study, and is believed to change in the presence of the independent variable. It is the "presumed effect."

Bar chart

Used to summarize the frequency of discrete and categorical data that are distributed in whole units or classes Bar charts are used to summarize discrete and categorical data - similar to histograms except the bars are separated to indicate discrete units or classes

Pie Chart

Used to summarize the relative percent of discrete and categorical data into sections

Quantitative Variable

Varies by amount. This variable is measured numerically often by counting or measuring ex. food intake in calories (continuous variable) or food intake by pieces of food consumed (discrete variable) - both measured by amount (numeric units) p.20 for examples

Qualitative Variable

Varies by class. This variable is often represented as a table and describes nonnumeric aspects of phenomena ex. upper class / lower class, unipolar / bipolar, man / woman p.20 for examples

Relative percent

a summary display that distributes the percentage of scores occurring in each interval relative to all scores distributed sums to 100%

Relative Frequency

a summary that distributes the proportion of scores in each interval. It is computed as the frequency in each interval divided by the total number of frequencies recorded sums to 1

Open interval

an interval with no defined upper or lower boundary

Proportion

is part or portion of all measured data. The sum of all proportions for a distribution of scores is 1.0

frequency

is the number of times or how often a category, score, or range of scores occurs

IQR

is the range of values between the upper(Q3) and lower(Q1) quartiles of a data set

Continous Variable

measured along a continuum at any place beyond the decimal point. A continuous variable can thus be measured in fractional units ex. Olympic sprint times p.20 for examples

Discrete variable

measured in whole units or categories that are not distributed along a continuum ex. Number of siblings, socioeconomic class, etc. p.20 for examples

Ratio Scale

measurements that have a true zero and are distributed in equal units The most informative scale of measurement - there are no restrictions for variables measured on a ratio scale ex. age, numbers, money, etc.

Interval width

range of values contained in each interval of a grouped frequency distribution

Ungrouped data

sets of scores that are distributed individually, where the frequency for each individual score is counted. Data are typically ungrouped for data sets with only a few different scores and for qualitative or categorical variables. Grouped data have intervals, ungrouped data do not

Median

the middle value in a distribution listed in numeric order Outliers influence the value of the mean but not the median The 50th percentile of a cumulative percent distribution can be used to estimate the value of the median Typically used to describe skewed distributions and ordinal scale data

Population Size

the number of individuals who constitute an entire group or population. Represented by: N

Sample and Population mean

the respective means (the notation is slightly different)

Percentile Point

value of a score on a measurement scale below which a specified percentage of scores in a distribution fall The 75th percentile point is the value below which 75% of the scores in a distribution fall (percentile rank)

True Zero

when the value of zero truly indicates nothing on a scale of measurement. Interval scales do not have a true zero