Stats test 1

Descriptive statistics

organize and communicate a group of numerical info using a single or few numbers

Inferential statistics

draw conclusions about the real world based on smaller sample sizes of that population

Sample

subset of observations drawn from the population of interest; used for studying

Population

collection of all possible members of an entire group; individuals

WEIRD population

a population that doesn't take into account cultural differences

Hypothetical construct

an abstract idea or concept we want to understand

Operational definition

a specific tangible measureable thing we measure or manipulate

Variable

any observation of a physical, attitudinal or behavioral characteristics that can take on a different variable

Discrete observation

variables that only take on specific values; cannot be divided infinitely (ex: what color, letter grade, gender)

Continuous observation

variables that can take on a full range of values; can be divided infinitely (ex: how many points did I get in class, weight, temperature)

NOIR

the four levels of measurement: Nominal, ordinal, interval, ratio

Nominal

used for observations that have categories or names as values

always discrete, never continuous

Ordinal

used for observations that have rankings, order of the label matters (ex: 1st, 2nd, 3rd, in no world does 3rd come before 1st)

always discrete, never continuous

Interval

used with numbers that are equally spaced, have to know the distance between variables from only looking at the number itself, scale must be evenly spaced NOT the data

sometimes discrete, sometimes continuous

Ratio

like interval but has a meaningful zero point; if the variable's measured point is zero the thing does not exist, ratio test - if you take twi measurements and divide them by itself it should make sense (ex: money - $0 money doesn’t exist and $50 is half of $100)

rarely discrete, almost always continuous

Reliable measure

a measure that is consistent

Valid measure

a measure that measures what it was intended to measure

what is a good measurement

both reliable and valid

Descriptive method

observe and describe behavior; each observation is a single variable

Correlational method

predictive relations between variables in naturally occurring groups; cannot determine the cause of an observed effect (correlation does not equal causation) two variables, no random assignment and no control both variables are correlational methods

Experimental method

causal relations between variables through manipulation and control, need random assignment, two variables but controlling

Experiments

a study in which participants are randomly assigned to a condition or level of one or more independent variables

Random assignment

every participant in a study has an equal chance of being assigned to any of the groups

Self-selection into groups

not the same as an experiment

Independent variable

the variable that is manipulated by the researcher; defines the groups that are being compared

Dependent variable

the variable that the researcher measures; the thing you are comparing across different groups

Constant

data that doesn't change

Frequency table

most basic way to visually describe one variable; two columns of variable name and frequency

Grouped frequency table

groups of values showing the frequency of observations falling within an interval

Histogram

a grouped frequency table presented visually; often used when data is continuous, when data covers a wider range

Symmetrical distribution

a distribution shape where both sides mirror each other

Positively skewed distribution

a distribution shape with a tail pulled toward the higher (positive) end

Negatively skewed distribution

a distribution shape with a tail pulled toward the lower (negative) end

Unimodal

a distribution with one peak

Bimodal

a distribution with two peaks

Multimodal

a distribution with many peaks

Rectangular

a distribution with no peaks

Kurtosis

how fat or skinny a distribution is

Leptokurtic

skinnier than normal distribution, also known as positive kurtic

Platykurtic

fatter than normal distribution, also known as negative kurtic

Pareto chart

a special case of a bar graph arranged based on the bars' height

Box plot

a chart dividing data into quartiles, continuous vs discontinuous

Violin plot

two histograms mirrored around a box plot

Line plot

charts used to illustrate the relation between two continuous (scale) variables;

scatter plot

in a scatter plot each dot is a data point, a type of graph that uses dots to show the relationship between two different numerical variables

Biased scale

using scaling to skew results

Sneaky sample

occurs when participants are preselected or self-selected to provide data

Interpolation

assuming that values between two data points follow the same pattern, assuming coninuity in the data when you dont actually know what happens

Extrapolation

assuming that values beyond the data points will continue indefinitely, trend that exists now is a summary of what has happened in the past

Inaccurate values

using scaling (like a truncated y-axis) to distort portions of the data

Central tendency

where the middle of the data points is; the most important way to talk about outcomes, best way to represent smth we mesured is middle value in someway

Mode

the most frequently occurring score in a distribution (where multimodal comesfrom)

Median

looking at the entire range in order and finding what falls in the middle - skewed

Mean

adding up all scores and dividing by the number of scores you have (the average) even

Statistic

any number that you calculate from a sample latin letter

Parameter

a number based on the whole population greek letter

Variability

a numerical way of describing how much spread there is in a distribution

Range

the highest score minus the lowest score

Variance

the average squared deviation from the mean

Standard deviation

the variation from the simple mean; typical amount that scores vary or deviate from the sample mean

Deviation from the mean

the amount that a score in a sample differs from the mean of the sample

Sum of squares (SS)

the sum of each score's squared deviation from the mean

Quantiles

dividing a distribution into quarters (Q1 = 25%, Q2 = 50%, ….)

Interquartile range (IQR)

the difference between the 75% score and the 25% score

when is range weak

if you have extreme data points

what is the middle line in a box plot

the median

Probability's three rules

the probability of a thing is between 0% and 100%; something must happen (P=1); for two things that cannot happen together - the chance that either happens is the sum of their probabilities

Conditional probability

given a precondition what is the probability of a particular thing

Probability

the proportion that we expect to find in the long run (theoretically if we do it forever)

Proportion

the number of successes divided by the number of trials

Percentage

a probability or proportion multiplied by 100

Random sample

every member of the population has an even chance of being selected into the study

Convenience sample

a sample that uses participants who are readily available (what most samples are)

Generalizability

applying a sample to another context; can be improved by validation

Inferential statistics

techniques to extrapolate information from a smaller sample to make predictions and draw conclusions about a larger population

Null hypothesis

the assumption of no effect or no difference; whatever you're trying to measure you assume you’re wrong or that the difference is in the opposite direction

Alternative (research) hypothesis

the belief that you are right, what you believe, there is a difference

Proof by contradiction

divide into two possible scenarios (H0 and H1), assume H0, use data to prove yourself wrong, if you counter a contradiction you reject your assumption

Proof by improbability

see if ravens are black or not, assume all ravens are not black, find 100 ravens that are black, improbable that all ravens are not black, how likely are things to happen or be related to each other

Reject the null hypothesis

the decision made when the data suggests there is a mean difference; conclude a difference is found

Fail to reject the null hypothesis

the decision made when we fail to find a mean difference; conclude no difference is found

Type 1 error

rejecting the null hypothesis when it's true (saying something happened when it didn't) (bad liar)

Type 2 error

failing to reject the null hypothesis when it's false (saying nothing happened when it did) (shit idiot)

Standards

without standardization extra effort is needed to understand context; common standards include percentiles and ranks, percentiles aren’t super flexible

Normal curve

a very specific bell-shaped curve that is unimodal, symmetric and defined mathematically, if you are perfect average you are 0 standard deviations away from the mean

Z score

number of SD your score is away from the mean, provides ability to convert any variable to a standard distribution, allows for comparison, gives us a sense of where a score falls in relation to mean of population, can be transformed into percentiles

Standardization

converting individual scores from different distributions into a shared normal distribution with a known mean

Calculating Z score step 1

subtract the mean of the population from the raw score

Calculating Z step 2

divide the result by the standard deviation of the population (Z = (x − μ) / σ)

Transforming Z into a raw score

multiply the z-score by the population standard deviation, add pop mean to this product, (x=z(σ)+μ)

Benchmarks

the standard normal curve's fixed percentages under different parts of the curve

Unit normal table

a table used to look up the proportion of a distribution above

likelihood of drawing a score between 0 and 2 is what

48%

more extreme

further away from zero

when you go from a sample to mean of sample when is it safe to assume normal distribution of means

as long as u measure from about 30 people

Central limit theorem

the distribution of sample means is normally distributed when samples are large, the more things that contribute to an outcome the more likely it is to be normally distributed

Distribution of sample means

has the same mean as the population; most samples will be near the mean; the larger the sample size the closer most means should be to population mean, normal distribution if population distribution is normal or if n is relatively large (central limit theorem)

Standard error

the standard deviation of the distribution of sample means; applies specifically to the distribution of sample means (σM = σ / √N, estimated with Sm = s/√N)

Percentile

what proportion of the data is below a given point

Z statistic (Z-sample)

like a z-score but for a group or sample mean instead of an individual score; means are used rather than individual scores