UofT PSY201 - Midterm 1

statistics

refers to a set of mathematical procedures for organizing, summarizing, and interpreting information

2 purposes of statistics

1. used to organize and summarize the info so that the researcher can see what happened in the study and communicate these findings to others

2. help the researcher answer the questions that initiated the research by determining exactly what general conclusions are justified based on the specific results that were obtained

Population

the set of all the individuals of interest in a particular study.

- varies in size

Sample

a set of individuals selected from a population, usually intended to represent the population in a research study.

- when a researcher finishes examining the sample, the goal is to generalize the results back to the entire population

random sample

In a random sample everyone in the population has an equal chance of being selected.

Variable

A variable is a characteristic or condition that changes or has different values for different individuals.

Data

Data (plural) are measurements or observations.

Datum (score/raw score)

A datum (singular) is a single measurement or observation and is commonly called a score or raw score.

Data Set

A data set is a collection of measurements or observations.

Parameter

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

Statistic

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

descriptive statistics

statistical procedures used to summarize, organize, and simplify data

inferential statistics

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

sampling error

the naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter

WEIRD Samples

Western, Educated, Industrialized, Rich, Democratic

discrete variable

Consists of separate, indivisible categories. No values can exist between two neighbouring categories.

ex. countries, types of dogs

continuous variable

a quantitative variable that has an infinite number of possible values that are not countable

ex. height weight

real limits of a continuous variable

those values that are above and below the recorded value by one-half of the smallest measuring unit of the scale

lower/upper real limits

lecture 1-6, 05:30

Nominal scale of measurement

measurement in which numbers are assigned to objects or classes of objects solely for the purpose of identification

1 - blue

2 - green

3 - brown

lecture 1-7

ordinal scale of measurement

a scale of measurement in which the measurement categories form a rank order along a continuum

ex. rank your experience on a scale of 1-10

possible inconsistent 'distance' between 1, 2, 3, 4...

interval scale of measurement

Highest form of measurement and meets all of the rules of other forms of measurement: mutually exclusive categories, ordered ranks, equally spaced intervals, and a continuum of values. Arbitrary zero.

ex. temps from -30 to 50; Celsius, Fahrenheit

ratio scale of measurement

All of the same in interval, except there is the addition of a true-zero point.

Ex. height, weight, time on task, income, age, Kelvin

correlational research

the study of the naturally occurring relationships among variables

experimental research

gathering primary data by selecting matched groups of subjects, giving them different treatments, controlling related factors, and checking for differences in group responses

do changes in one variable cause changes in another variable?

needs IV and DV

construct

internal attribute that cannot be directly observed but is useful for describing and explaining behavior

Non-equivalent groups

Possible confounding variable in which two or more groups in an independent samples design experiment differ on a skill or characteristic relevant to the dependent variable

lecture 1-8

pre-post study

Quasi-experimental and nonexperimental designs consisting of a series of observations made over time. The goal is to evaluate the effect of an intervening treatment or event by comparing observations made before versus after the treatment.

X or Y

individual measurements or raw scores

N

number of scores in a population

n

number of scores in a sample

sigma

summation

sigmaX

add all scores for variable X

parametric statistics

A branch of statistics which assumes that sample data comes from a population that follows a probability distribution based on a fixed set of parameters. More precise.x

Non-parametric statistics

Testing not based on population parameters

includes tests of significance based on nominal or ordinal data

Used when parametric assumptions cannot be met

Less powerful than parametric stats

More difficult to reject null hypothesis

Can be use with small sample and nominal or ordinal data

frequency distribution

an arrangement of data that indicates how often a particular score or observation occurs

proportion

the fraction of the total group associated with each score

p = f/N

percentage = f/N(100)

cumulative frequency

number of scores at or below a given score

cumulative percentage = cf/N (100)

percentiles for grades^

ordinate

y-axis

2/3 of x axis

start at 0

abcissa

x-axis

Histogram

A graph of vertical bars representing the frequency distribution of a set of data.

interval or ratio data

Polygon

dotted line graph

dot in the centre of each interval

interval or ratio data

bar graph

A graph that uses horizontal or vertical bars to display data

histogram with gaps between different bars

Nominal or ordinal data

relative frequency

the fraction or percent of the time that an event occurs in an experiment

describes ratio between frequencies rather than actual values to compare

Shape of Distribution

Symmetric, right-skewed (with a heavier right tail), or left-skewed (with a heavier left tail).

bell shaped/normal/Gaussian(mesokurtic)

platykurtic/leptokurtic (kurtosis)

central tendency

mean, median, mode

mean

average

population mean (mu) = sigma(X)/N

sample mean (x-bar) = sigma(X)/n

for interval or ratio scale

"balance point" of distribution

do not use mean with nominal scale, skewed dist, or when values are missing

affected by every score

used when you know the value of every score and can calculate sigmaX

Median

the middle score in a distribution; half the scores are above it and half are below it

cuts the area of the distribution graph in half

middle of the distributions in terms of scores

unaffected by extreme scores

ordinal, interval, and ratio data

used with skewed distribution, open ended dist and undetermined values

Mode

the most frequently occurring score(s) in a distribution

peak in a graph

used with any scale

used for discrete variables, describing shape, as a supplementary measure

ONLY ONE for nominal scale

bimodal (2 modes), multimodal (3+ modes)

major mode/minor mode^

weighted mean

the mean obtained by assigning each observation a weight that reflects its importance

sigmaX1 + sigmaX2 / n1 + n2

Variability

in a set of numbers, how widely dispersed the values are from each other and from the mean

range

the difference between the highest and lowest scores in a distribution