psyc011 week 1

chapter 1

part 1

• famous statisticians

  • karl pearson - chi square to decide among theories

  • ronald fisher - experiments w random assignment

  • jerzy neyman & egon pearson - NHST

  • jacob cohen - effect sizes & power

  • geoff cumming - the “new” stats

  • john kruschke - bayesian stats

• field of stats is a human endeavor designed to help people develop reasoned beliefs about variable processes

• descriptive statistics - number that conveys a particular characteristic of a set of data

  • ex) mean - arithmetic average; sum of scores divided by number of scores

• inferential statistics - method that uses sample evidence and probability to reach conclusions about unmeasurable populations

  • AKA smaller size of population too big

• null hypothesis statistical testing (NHST) - technique producing probabilities accurate when the null hypothesis is true and certain assumptions are met

part 2

• population - all measurements of a specified group

  • sample - measurements of a subset of a population

• parameter - numerical or nominal characteristic of a population

• statistic - numerical or nominal characteristic of a sample

• variable - something that exists in more than one amount or in more than one form

• quantitative variable - variable whose scores indicate different amounts

  • continuous variable - a quantitative variable whose scores indicate different amounts

    • note** these can identified by being able to have half numbers (ex. you can have a 9.5 shoe size or get somewhere in 1.5 hours)

  • discrete variable - variable for which intermediate values between scores are not meaningful

    • note** these can be identified by not being able to have a half number (ex. you cant have half a student in a class)

• categorical variables - variable whose scores differ in kind, not amount

  • ex) race, religion, college major

part 3

• scales of measurement

  • nominal scale - measurement scale in which numbers serve only as labels and do not indicate quantitative relationship

    • ex) yes/no responses, colors (blue, green, red)

  • ordinal scale - measurement scale in which numbers are ranks; equal differences between numbers do not represent equal differences between the things measured

    • ex) bachelor’s, master’s, PhD

  • interval scale - measurement scale with meaningful intervals but no true zero point

    • ex) zero in celsius vs fahrehnheit

  • ratio scale - measurement scale with meaningful intervals and a true zero point

    • height, weight, age

• experimental design

  • independent variable - variable controlled by the researcher

  • dependent variable - observed variable that is expected to change

  • level - one value of the of the independent variable

  • treatment - one value/level of the independent variable

    • its basically like the most extreme level

  • extraneous variable - variable other than the independent variable that may affect the dependent variable

• Epistemology - study or theory of nature of knowledge

  • epistemology aims to answer

    • what do we know

    • what does it mean to say that we know something

    • what makes justified beliefs justified

    • how do we know that we know

• steps to statistical analysis

  • 1) explore data

  • 2) answer the question - what are the effects that chance could have on the descriptive stats I calculated?

  • 3) write the story explaining the relationships in the data

chapter 2

part 1

• simple frequency distribution

  • 1) find lowest and highest scores

  • 2) in columns, write all numbers from greatest to least

  • 3) name the column

  • 4) start w number in upper left, draw line under it, tally mark beside number in column

  • 5) continue underlining and tall

• computational tools

  • R, MATLAB, Excel or sheets, python, SAS, SPAA, etc

  • in this class, jamovi (free, based on R, similar to SPSS)

part 2

• symmetric distributions

  • normal distribution (normal curve) - graph of observed scores with particular shape

  • rectangular distribution - occurs when frequency of each value on x-axis is the same

• asymmetric distributions

  • skewed distribution - could be + or -

  • positive skew - graph with high amount of low scores

    • graph stretched most on left side

  • negative skew - graph with high amount of high scores

    • graph stretched most on right side

• bimodal distribution - distribution with two modes (2 high points)

• line graph - graph that uses lines to show relationship between 2 variables

chapter 3

part 1

• central tendency - descriptive statistics that indicate a typical or representative score

  • mean - arithmetic average; sum of scores divided by number of scores

  • median - point that divides a distribution of scores into equal halves

  • mode - score that occurs most frequently in a distribution

  • weighted mean - overall mean calculated from two or more samples with different Ns

part 2

• median - point that divides distribution of scores into two equal parts

• finding median:

  • order scores greatest to least

  • median itself should have equal number of scores above and below it

    • if odd # of scores, median in the middle

    • if even, median halfway between middle 2 (add both scores and divide by 2)

• mode - most frequently occurring score; score observed most often

• scale of measurement

  • interval or ratio - mean, median, mode

  • ordinal - median or mode

  • nominal - mode only

• skewed data

  • if data very skewed, median may be better than mean

  • EX) income - mean $83K, median $59K

• open-ended class intervals

  • ex) “75 and over” or “$200K or more”

• estimating answers

  • estimating helps you think the problem through

  • estimates help you catch errors when compared to computer output

  • catching errors increases your credibility

chapter 4

part 1

• variability - having a range of values

  • think of it as differences

• to summarize group of numbers

  • 1) how big or small or the numbers?

  • 2) are the numbers mostly close to each other or far apart?

• range - highest minus lowest score

  • not very informative because only two scores matter in its computation

    • drastically different distributions can give rise to same mean and range

• interquartile range - the middle 50% of the observations

  • used to avoid instability of the range statistic

  • just trimmed off top and bottom 25% of data

• to find interquartile range, must find 25th and 75th percentile

• percentile - point below which a specified percentage of distribution falls

part 2

• standard deviation - descriptive measure of the dispersion of scores around the mean

  

• deviation score - raw score minus the mean of its distribution

  • just says how far a score is from mean

part 3

• use definitional formula being given in class, not raw formula from computer

• graph standard deviation using error bars but clarify range

chapter 5

part 1

• z score - score expressed in standard deviation units

  • they are comparative, dependent on all other scores

  • as descriptive stat, vary from -3 to +3

• standard score - score expressed in standard deviation units; z is one example

  • ex) IQ scores, z scores,

part 2

• outlier - extreme score separated from others and at least 1.5 * IQR beyond the 25th or 75th percentile

• elements of boxplot

  • boxplot - graph that shows a distribution’s range, IQR, skew, median, and sometimes others

  • median - line in middle of box

  • mean - dot in box

  • 25th percentile - bottom or left side of box

  • 75th percentile - top or right side of box

  • whiskers - extend to lowest and highest scores in distribution

  • central tendency - mean or median

  • variability

    • IQR - size of box

    • distance between end of whiskers

  • skew

    • position of mean relative to median

    • relative length of the whiskers

• effect size index - amount of degree or separation between two distributions

  • use whatever units make most sense

  • when scale is unfamiliar, use standard statistic “d”

• descriptive statistics report

  • table showing mean, median, percentiles, effect size, etc