Statistics Flashcards
What is statistics?
A branch of mathematics devoted to the collection, analysis, interpretation, and presentation of data
What is a population?
Set of all individuals of interest in a particular study, entire group of interest, usually quite large
What is a sample?
Set of individuals selected from a population, subset, purpose is to represent population
What is a measurable quality of a population called? What are they represented by?
parameter, greek letters (mu/sigma)
What is a measurable quality of a sample called? What are they represented by?
statistic, english letters (m, s)
What does descriptive statistics do?
describe and present data using graphs etc
What does inferential statistics do?
Generalize from samples to populations, make predictions (t-tests, ANOVA)
What is sampling error?
Natural differences that exist, by chance, between a sample statistic and a population parameter
What is the experimental method?
goal is to demonstrate a cause-and-effect relationship, involves manipulation/control
What are extraneous variables?
variables that are not of interest to the researcher in a particular study but could influence the dependent variable
What are some examples of participant variables?
age, gender, education level, IQ
What are some examples of environmental variables?
lighting, time of day, and background noise/distraction
What is random assignment?
Each participant has an equal chance of being assigned to each of the treatment conditions or groups
What is matching?
Used to ensure equivalent groups or equivalent environments
What is holding constant?
hold extraneous vairbale constant across all gorups
What are non-experimental methods?
no ability to control which participants go in what group
ex. surveys, correlational research, observational research
What is the independent vairbale called in non-experimental studies?
qausi-independent variable
What are discrete variables?
Separate, indivisible categories, no values between categories (no decimals)
Ex. number of children, number of siblings, number of pets
What are continuous variables?
Infinite number of possible values that fall between any two observed values (decimals)
Ex. height, weight, skull circumference etc
What are the four scales of measurment in order of least to most compelx?
nominal, ordinal, integral, ratio
WHat is nominal?
non-numerical, qualitivative categories
ex. eye colour
What is ordinal?
ordered attributes wiht no known differences between values
ex. likert scale, race results, clothing size
What is integral?
ordered attributes with known differences but no true 0
ex. temp in C, IQ, SAT score
What is ratio?
orderd attributes with knwon differences and true zero
ex. temp in K, height, weight
What are frequency distributions?
method to organize/simplify data, can be a table or a graph
What is always included in a freuqneyc distribution?
set of cateogires, and the frequency/number of indivuals in that category
What does the sum of frequncies need to equal?
N (total number of participants0
How can you calculate propotion? What should they add up to?
p=f/N
add up to 1
How can you find the percentage using the proportion?
multiply by 100
How do you use frequency table to calculate mean?
add the number of each participant in each category (so if category=9 has frequnecy of 3, you need to add 9, 3 times)
What is a grouped frequency distirbution? Why is it used?
column X shows groups of scores (ex. 1-10)
use when set of scores if too large
What are pros/cons of grouped frequency disttibution?
pro: easier to read/understand
con: some info is lost when categories are grouped
When are histograms appropiate? What else would be acceptable?
for integral/ratio data
frequency polygon
When are bar graphs appropiate?
for nomial/ordinal data
WHat are the 3 characterisitcs of frequency distributions?
shape, central tendency, variability
When are distributions said to be skewed?
if scores are mostly on one side
What does a positive skew look like?
most scores are on lower/negative side and the tail tapers towards posititvw
What does a negative skew look like?
most scores are on higher/positive end and tail tapers towards negative
How can you check if data is normally distirbted?
can use histograms, numerical descriptives, shaprio-wilk test
What is the purpose of measuring central tendency?
Find single score that is most typical/representative of entire group
What is mean?
arithmatic average of set of scores/values
If data is perfect what measure of central tendency should we use?
mean (strongest method)
How adding/subtracting a constant from each score affect the mean?
mean changes by same constant
What does multiplying/dividing each score by same constant affect mean?
mean is multiplied/fivided by wsame constant
What is the median?
midpoint of the data (from smallest to largest)
If you are finding the median what do you do when there are an odd number of scores?
add middle 2 scores and didivide by 2
What is mode?
number that is most frequent
What measure of central tendency can you have multiple answers for?
mode
What definition are we using for mode in this course?
strict (only bimodal if both modes have same frequency)
When should the median be used over the mean?
when there are extreme scores/skewed distribution, undetermined values, open ended distributions, ordinal data
When should the mode be used?
nominal scale
What is mean, median, mode in symettrical unimodal distribution?
mean=median=mode
What is mean, median, mode in symettrical bimodal distribution?
mean=median, but not mode
What is relationship of mean, median, mode for positive skew distribution?
mode<median<mean
What is relationship of mean, median, mode for negative skew distribution?
mode>median>mean
What is range? What is the equation?
Distance covered by scores in distribution forms smallest to largest score
range = Xmax - Xmin
Where does summation go in bedmas?
after multiply/divide (BEDMSAS)
How do you calculate variance for sample?
s^2= summation of (x-m)^2/n-1
What is variance?
average squared distance from the mean
How does the variance differ between a sample and a population?
samples tend to have less variability
How does the variance equation change for a population?
denomitaor is just N not (n-1)
What does degree of freedom mean?
the number of independent variables that can vary in an analysis without breaking any constraints
How do you find the standard deviation?
take the square root of the variance
How does adding/subtracting a constnat from each score change the standard deviation?
std will not change, (b/c each score remains at same distance from mean)
How does multiplying/dividing a constant from each score change the standard deviation?
will multiply/divide std by same constant
What do z scores do?
locate the location of a score in a distribution
What does the sign of a z score tell you?
+ means above the mean, - means below the mean
What does the mean always equal in z scores? What about std?
0, 1
WHat is the formula for z score?
z= (score - mean)/std
What do standarized distirubution look like compared to the original data?
graph has same shape, score is in same lcoation just renamed
How would you find what the new score would be given the old and new distributions mean and std and the old score?
convert old score to z score in old distribution, then plug that z score into X= mean + (z*std), using mean and std of new distribution
