intro to stats

Question 1

categorical variables

Answer 1

Variable varies by type
- Levels are usually string-based (character-based)
- Can be numerical if the numbers are used as names (no numerical value associated with the number)

Question 2

integer variables

Answer 2

• Numerical variable consisting of whole numbers
• Numbers have real numerical meaning

Question 3

continuous variables

Answer 3

• Numerical variables which can theoretically have infinite decimal places

Question 4

Dichotomous variables

Answer 4

• only 2 levels
• 0/1, Ctrl/Treatment, TRUE/FALSE
• Can be categorical or integer
  Variables defined by data type

Question 5

nominal variables

Answer 5

categorical variables

Question 6

ordinal variables

Answer 6

ranked data
ex. 1st, 2nd, 3rd

Question 7

interval and ratio scale variables

Answer 7

can be integers or decimal places
ratio : true zero, ratios can be meaningfully calculated (ex. 0K is absence of heat)

interval: does not have true zero,(0C is not absence of heat)

Question 8

variables defined by casual relationship

Answer 8

In an experimental setting, we manipulate the independent variable, and measure scores for the dependent variable

Question 9

nuisance variables

Answer 9

• confounding variables can potentially change the value of the outcome variable, and vary systematically with the predictor variable
• obscuring variables can also potentially change the value of the outcome variable, but do not vary systematically with the predictor variable

Question 10

experimental designs 1

Answer 10

Different individuals are in different experimental conditions
* Between-subjects designs
* Independent groups designs

Question 11

experiment designs 2

Answer 11

The same individuals are in different experimental conditions
* Within-subjects designs
* Repeated-measures designs

Question 12

mixed designs

Answer 12

some predictor variables are between-subjects and some are within-subjects

Question 13

inference

Answer 13

based on various methods such as hypothesis testing,
confidence interval estimation and parameter estimation

Question 14

inferential statistics

Answer 14

uses sample statistics to estimate the value of a population parameter

Question 15

parameter

Answer 15

a constant numerical characteristic of a population
- can include shapes (normal distribution), as shapes can be defined numerically

Question 16

statistic

Answer 16

corresponding value calculated for a sample

Question 17

population parameter and sample statistics symbols

Answer 17

standard deviation
- sigma: population parameter
- s: sample statistic

mean
- mu: population parameter
- M: sample statistic (or x bar)

Question 18

i

Answer 18

index or individual
- refers to each score

Question 19

statistics are invented tools

Answer 19

• statistical tools are invented to estimate probabilities that guesses are correct

Question 20

characteristics of popular statistical methods

Answer 20

• common sense
• ease of use
• inertia (being good enough)

Question 21

x^2

Answer 21

test statistic is a single number that represents how well the observed data fits your null hypothesis
-needs to produce a single number that incorporates two properties of the data(number and proportion)

Question 22

probability distribution

Answer 22

divide counts (y) by the total number of simulations
- used to obtain probabilities associated with specific outcomes

Question 23

p value

Answer 23

probability of obtaining our observed results if H0 was true
- p value low = low probability of obtaining our observed results, if H0 is true

Question 24

classical statistics

Answer 24

calculates the theoretical probability distribution that would be obtained if the null hypothesis is correct
ex. df= k-1

Question 25

simulation vs. classical statistics

Answer 25

theoretical
- any value of x^2 is possible, probability distribution is continuous

simulation based
- limited number of x^2 values possible
- small number of possible outcomes when counting numbers of heads/tails from 100 coin tosses
- probability distribution is discrete

simulation based are better, only deal with possible outcomes
- but classical stats are more widespread

Question 26

how can we assess variability amongst a set 6 scores?

Answer 26

• calculate difference between each score and a single point
• difference between each score and the mean
• DEVIATION SCORE (xi -x bar)

Question 27

how to calculate mean deviation?

Answer 27

1. ignore the signs (mean absolute deviation)
2. remove the signs by squaring all deviation scores, calculating the average, then taking the square root (standard deviation

Question 28

MAD vs standard deviation (s)

Answer 28

• outliers will distort estimates of s more than MAD- larger deviation scores get even larger when squared
• MAD is more intuitive cause s is result of squaring, adding, square-rooting
• in real datasets, MAD estimates from a sample may be better estimates of the underlying population parameter than s

S
- s is one of the parameters used to define the normal distribution, which is centrally important in classical statistics
- Fisher (1920) demonstrated that in a perfect normal distribution, sample s is a better estimate of population standard deviation compared with sample MAD as an estimate of population MAD (s estimates its corresponding parameter better than MAD)

s is the dominant measure of variation used in stats

Question 29

standard deviation (s)

Answer 29

s and variance (s^2) are primary measures of variation

divide n-1 (degrees of freedom)

s= dividing the sum of squares by the degrees of freedom, then taking the square root

mean deviation score is calculated by summing the squared deviation scores, then dividing number of scores that vary, then taking the square root

Question 30

df

Answer 30

first calculate sum of squares (SS): sum(xi-x bar)^2

df (number of things that can vary): n-1

Ex = n x x-bar

purpose of s= generate estimate of average variation

Question 31

normal distribution

Answer 31

natural variables commonly approx to normal distribution
errors of measurement commonly approximate to the normal distribution
means calculated from multiple samples drawn from pop will approx to normal distribution

is a probability distribution
- common use: derive probability that a score selected at random from normal-distributed pop will have a specific value

Question 32

reading the normal distribution

Answer 32

distribution
y axis: ignore values
- for most plots: interested in value of y that corresponds to a value of x
- probability distrubtions: interested in area under the cure between two variables of x, and express it as the percentage of total area under the curve

x-axis: number of standard deviations from the mean
- standard deviation: average deviation from the mean

Question 33

summary of normal distribution

Answer 33

originated from attempts to stop disputes between gamblers

distrubtion is an approx of the binomial distribution with a large number of trials (games) and can be calculated simply from mu and s

combo of mathematical simplicity and usefulness of the normal distribution in modelling real variables and errors resulted in it holding a central position in classical statistics

if we know a population mu and s, and know that the variable is normally distributed, we can easily estimate the probability that a score will be within a specific range of values