Psycstat exam #1

population vs. sample

population: entire group of individuals

sample: individuals selected to represent population

parameter

describes population

statistic

describes sample

discrete variables

invariable categories

• ex: dice roll

continuous variable

infinitely divisible

• ex: time or weight

nominal scale

unordered set of categories, identified by name only

• ex: I like hamburger. I like milkshake.

ordinal scale

ordered set of categories

• ranking but no amount of diff between ranks

• direction of diff between two individuals

• ex: race - 1st, 2nd, 3rd

interval scale

ordered series of equal-sized categories

• direction & magnitude of difference

• zero point located arbitrarily - doesn’t mean lack of _, just means 0 recorded/measured - meangingless

• ex: race w/ time and distance, IQ test, temp

ratio scale

interval scale w/ true zero meaning nothingness

• direction & magnitude of diff, ratio comparisons of measurements

• ex: books read this year, height (can be 0)

correlational study

doesn’t provide explanation for relationship

• one group w/ 2 variables measured for each individual

experimental study

1 variable manipulated while another observed

• cause & effect - identify causation

• individual relationship

• always has IV & DV

nonexperimental study

• no variable manipulated or random assignment

• unclear IV & has DV

N

# of scores in population

n

# of scores in sample

frequency table

• 2 columns

  • x column: values within range of scores

  • f score: # of times x score appears

• purpose: organize & simplify dataset

grouped frequency distribution table

• lists groups of scores

• intervals have the same width

bar graph

• nominal or ordinal scale

• gaps between bars

histogram

• interval or ratio

• height corresponds to frequency

• continuous variables

• no gaps between bars

  

polygon

• interval or ratio

• continous line draw from dot to dot

• line from x-axis (zero freq)

stem and leaf displays

stems - first digits

leaves - last digits

proportion (p)

p = f/n

Normal Curve (AKA Normal Distribution)

symmetrical, greatest freq in center, decrease away from center

• multidetermined

• ex: IQ scores

central tendency

uses single value to describe center of distribution

• can compare 2 or more sets of data by comparing means

descriptive stats

describe set of data in simple, concise form

mode

most frequently occurring score or class interval, high point

• nominal, ordinal, interval, or ratio

• bimodal, multimodal

major mode

highest peak

minor mode

secondary peak

median

midpoint

• splits dataset in half - below/above

• list in order first

• relatively unaffected by extreme scores

mean

population: μ = ΣX/N

sample: M = ΣX/n

• balance point of distribution

• change value of any score, discard or add new scores change value of mean

when mean not representative

• few extreme scores

• very skewed

• nominal - no numerical meaning, order, scale

symmetrical distribution relationship

symmetrical distribution - mean = median

symmetrical distribution w/ 1 mode - mode = mean = median

shapes of distributions

positive skew

scores pule up on left side

negative skew

scores pile up on right side

S sample standard deviation

σ population standard deviation

SS (sum of squares)

SS = ∑(X - M)2

𝜎²

pop. variance

why divide by df for sample SD (s)

inflate estimate of variance so its more accurate

• df = n-1

Range (v1)

highest score - lowest

Range (v2)

lowest & highest score

why range is imprecise & unreliable

not all scores represented

most common measure of variability

standard deviation

standard deviation approximates

“avg’ distance from means for scores in dataset

each score multiplied/divided by constant

SD will also be multiplied/divided by same constant

z-score

• how far away a point is from mean as a proportion

• expresses data in terms of mean and SD

advantage of z-scores to compare populations

standardizes → compare distributions w/ diff. scales

0 z-score indicates

equal to mean

z-score for population

X = score from dataset

μ = pop. mean

σ = pop. SD

z-score for sample

X= score from dataset

M = sample mean

S = sample SD

descriptive z-score

describes exactly where each individual score’s located

inferential z-score

determines whether specific score is representative

• above or below 2 → extreme/unrepresenative

z-score & SD

doesn’t change shape of distribution or location of any scores

only scale changes

smooth curve

smooth lines - emphasize overall patterns in ideal pop. distribution

hypothesis test (z-score)

1) state hyp.

• H₀: μ_{treatmen t​}= μ_known​

• H₁: μ_treatment​ ≠ μ_known​

3) calculate z-score

• calculate std. error of mean (σ_M​)

• calculate z

4) make decision

• |z| ≥ |1.96|