Psyc305: Chapters 1-5

Statistics

a set of mathematical procedures for organizing summarizing and interpreting information

Population

the set of all individuals of interest in a particular study, example- Chinese Americans over 65

Sample

A set of individuals selected from a population intended to represent the population in a research study, Example 200 Chinese American participants over 65

random sample

a sample where everyone in a population has an equal chance of being picked to better represent a population

Variable

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

Data

measurements or observations

Data Set

a structured collection of measurements or observations, ex a chart of height and weight of kittens

Datum

a single measurement or observation, commonly called a score or a raw score

Parameter

a characteristic that describes a population, ex the average running speed of an 11 year old male in Virginia

statistic

A characteristic that describes a sample, ex the average speed of 30 11 year old males in a study

descriptive statistics

statistical procedures used to summarize, organize, and simplify data, ex averaging , tables, graphs

inferential statistics

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

Representative Sample

a sample that reflects general population, used in inferential statistics to better make generalizations about a population

sampling error

the naturally occurring discrepancy that exists between a sample statistic and the corresponding population parameter, ex a population with an average IQ of 100 but a sample with an average IQ of 107

Constructs

internal attributes or characteristics that cannot be directly observed but are useful for describing and explaing behavior, ex: self esteem or hunger

Operational Definition

identifies a measurement procedure for measuring external behavior and used the resulting measurements as a definition and a measurement of a hypothetical construct, Ex heart rate while giving a speech to measure anxiety levels

discrete variable

consists of separate indivisible categories. No values can exist between two neighboring categories, ex- number of students in a class (there can't be half a student) or majors of students

Continuous Variable

When there are an infinite number of possible values that fall between two observed values. Ex-time

Real limits

the boundaries of intervals for scores that are represented on a continuous number line. Located half way between scores, ex 49.5 and 50.5 are the limits for what counts as a score of 50

Nominal Scale

a set of categories that have different names. Measurements on this scale label categories as observations but do not make any quantitative distinctions between observations, ex hair color

Ordinal scale

consists of a set of categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size and magnitude ex. First, second, third

Interval Scale

consists of ordered categories that are all intervals of exactly the same size. Zero point on an interval scale is arbitrary and does not indicate a 0 amount being measured. - example temperature

Ratio Scale

an interval scale with an absolute 0 point representing nothing. Ratios of numbers reflect ratios of magnitude

Correlational Method

two different variables are observed to set wether there is a relationship between them

frequency distribution

an organized tabulation of the number of individuals located in each category on the scale of measurement

Two other measures besides frequency distribution that describe distribution of scores and can be incorporated into the table

Proportion and Percentage

Proportion

the fraction of the total group associated with each score, p= f/n

Percentage Formula

#=p(proportion)100

Percentile Rank

a particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value

Percentile

when a score is identified by its percentile rank, ex a score of 9 is within the 95th percentile

Cumulative Frequency

The accumulation of individuals as you move up the scale, listed as cf

Cumulative Percentage

shows the percentage of individuals as you move up the scale, listed as c%

Cumulative Frequency Formula

c%= cf/N(100%)

frequency distribution limits

Frequency distribution uses real limits when using continuous data because because it measures in intervals, Ex. X=8 could be 7.5 - 8.5

Another name for the X axis

abscissa

Another name for the Y axis

ordinate

Measurement Scales

how variables (x values) are categorized, counted, or measured

Two graphing options for data using interval or ratio scale

Histograms and Polygons

Characteristics of a Histogram

Made of bars, No spaces between bars

informal histogram

Instead of bars the graph consists of stacked blocks.

Characteristics of a polygon

Dots representing data, are placed through each score with a line going through, the line is ended by drawing it down to the x axis

What graph can be used for nominal or ordinal data?

Bar graph

Characteristics of a bar graph

For nominal scale there are spaces between bars to indicate separate categories and for ordinal it is because you can't assume the categories are the same size

What graphs can be used for population distribution?

relative frequency bar graphs and smooth curves (interval or ratio scale)

Normal Curve

a smooth curve graph with a single wide slope that is symmetrical on both sides, ex. IQ scores

Symmetrical distribution

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

positively skewed

tail moving towards the right

negatively skewed

tail going toward the left

Central Tendency

statistical measure to determine a single score that defines the center of a distribution of scores

•Goal is to find the most typical or representative value!

•Mean, median, & mode are most used

Mean

the sum of scores divided by the number of scores. Represented my M Xbar or mu

•Median:

The score corresponding to the point having 50% of the observations below it [and 50% above] when the observations are arranged in numerical order, does not always change when adding or dropping a score

When is the median preferred?

Ordinal data or continuous data that is skewed

•Mode:

The most commonly occurring score in a sample or population does not always change with new score or change in score

When is the mode preferred?

•A nominal (and sometime ordinal) scale

•Discrete variables

•The mode is also useful for describing shape when used along with the mean

List Mean, Median, and Mode in order of

Mean, Median, Mode

Examples of Mean

Report Card, Sports

Examples of Median

Household income, Salary

Examples of Mode

Retail sales, election voting

Variability

a group of quantitative measures of the differences between scores & describes the degree to which the scores are spread out or clustered together

What are the two purposes of variability?

1.Describes the distribution of scores

2. Helps determine how representative a score is to the entire distribution

Range Formula for discrete variables

Xmax-Xmin +1

Deviation

Deviation - the distance of a score from the mean• For populations, deviation score = X - μ• For samples, Deviation score = X - M

Sum of Squares

Sum of squares - the sum of the squared deviation scores• Represented by the symbol, SS, SS =Σ(X -μ)2

Variance

The average squared [raised to the second power] distance from the mean, Pop: SS/n Samp: SS/n -1

Standard Devation

Standard deviation - the square root of thevariance and provides a measure of the averagedistance from the mean

Standard deviation formula

o= sqrt Sum(X-M)^2/N

Degrees of Freedom

Degrees of freedom - the number of scores in thesample that are independent & free to vary

Z- Score

a measure of how many standard deviations you are away from the norm (average or mean)

Z score formula

z = (X - μ)/σ

Standardized (z) distribution

distribution - a symmetrical distribution composed of scores that have been transformed to create predetermined values for μ & σ.