Week 1: Descriptive Stats and Stat Inference

independent variables influence the

dependent

categorical variables

assigned numerals representing categories, limited in what you can do with them

2 types of categorical variables

nominal and ordinal

nominal

2 or more unranked categories

ordinal

2 or more ranked categories

numeric variables

numbers represent an amount/quantity and not a ranking

2 types of numeric variables

discrete and continuous

discrete

only takes on specific values within a given range, countable (number of falls, bp, gait speed)

continuous

scores can occur along continuum in theory (distance, ROM, strength)

what is continuous constrained by

precision of measuring instrument (cant do ms)

parametric testing

assumes sample data is normally distributed and bell shaped, more powerful and prefered

parametric testing 2 requirements

quantitative data and has normal distribution

nonparametric testing

no assumption about normality

what is nonparametric testing done with

categorical data, quantitative data that is not normal

visual checks for distribution/normality

histograms, stem and leaf, QQ plots

numeric checks for distribution/normality

frequency tables, skewness and kurtosis, KS, SW

normal distribution def

most scores are in middle, often assessed with a histogram

histogram

graph with observation on X axis and times of value on Y

skew

distribution is asymmetrical, normality is not met

positive skew

right skew, scores are bunched at low values

negative skew

left skew, scores are bunched at high values

kurtosis def

refers to peakedness and degree to which scores cluster at tails

positive kurtosis

too peaked, long tails

negative kurtosis

too flat, short tails

QQ plot

plots quantiles of variable vs quantiles of theoretical distribution

QQ plot y axis

expected info

QQ plot x axis

observed

normality of QQ plot is shown if

data fall along straight line on plot

KS and SW tests are for

testing if distribution significantly deviates from normal distribution

If p is less than 0.05

data is significantly different from normal, NOT normally distributed

if p is more than 0.05

data is not significantly different from normal, it is normally distributed

for small samples under 50 use

SW

for large samples over 50 use

SW or KS

3 things for central tendency

mean, median, mode

mode

most frequent score, summarizes categorical data well

median

middle score when you order data, useful with ordinal data or quant data

what is prefered for skewed data/outliers

median

mean

average score, stable in samples

downside of mean

not good for categorical data or quant data that is skewed or has outliers

if data has outliers, which is more reliable

median

5 measures of variability/dispersion

range, quantiles, variance, SD, coefficient of variation

Range

largest minus smallest

quantiles

splitting data into parts

-quartiles or percents

quartiles

3 values that split data into 4 even parts

lower (1st) quartile

median of lower hald

2nd quartile

median

3rd quartile (upper)

median of upper half

interquartile range

upper minus lower

deviance

how different each score is from center

sum of squares indicates

total dispersion, total deviance scores from mean

standard deviation

square root of variance

coefficient of variation (CV)

ratio of standard deviation to mean expressed as pecentage

CV formula

CV=100 X (SD/mean)

why does coefficient of variation not use units

helpful for comparing distributions from different samples that may have different means or units

Lower CV indicates

less relative variation and more stability

2 things for statistical inference (prediction)

probaility, sampling error

probability

likelihood an event will occur given all possible outcomes

sampling error

extent to which a statistic varies in samples taken from same population

z score

expresses a scrore in terms of how many SD it is away from mean

formula for z score

Z=X-X/S

5% of z scores lie where

beyond -1.96 and +1.96 (2.5 % on each side

smaller sampling error means

less difference between sample and population mean

standard error of mean (SEM)

SD of distribution of sampling distribution

SEM is an indicator of

how close sample mean is to the true population mean (lower value suggests that sample deviates less)

SEM calculation

S/squar root of n (population)

As population increases, what happens to SEM

gets smaller, which is good

confidence intervals

range within which we believe the true population parameter lies

95% CI means

we are 95% confident that the population mean lies within this range

CI calculation

CI=+/- z x SEM

null hypothesis (HO) means

theres no difference

alternative hypothesis (HA) means

there is a difference

Statistical tests are based on which hypothesis

null, rejecting or failing to reject it

if p is less than 0.05

reject HO and accept HA

-different exists

if p is greater than 5

fail to reject HO

-no difference

type I errors

reject HO when HO is true

-would make you do opposite of whats true

-saying theres a difference when there may not be

type II errors

fail to reject HO when HO is false

-say theres no difference but there is

power

probability of finding a statistical difference when one exists