STAT 100 Midterm 1

statistics

the science of variability

statistical investigative cycle

a lens that statiticians use to help them solve real world problems

steps of a statistical investigative cycle

1. problem- identify a statistical question

2. plan- chose a sample design, study design, and measures

3. data- collect and process data

4. analysis- look for patterns with summary tables, graphs, and statistical models

5. conclusion- interpret the results and generate new questions about the real world context

causal inferences

claims that some choice we make will cause some effect to happen

causal factor

the “initial”

outcome factor

the conclusion or the thing effected

claimed effect

the “arrow”

generalization inferences

claims about an entire group of people, based only on information from a sample of people

population of interest

the group of people it is trying to describe

attribute

the characteristic about them

What was compared?

“Was it apples-to-apples?”, related to CAUSAL claims, consider variability and uncertainty, internal validity

Who’s not here?

related to GENERALIZATION claims, how to question external validity

Data

a representation of someone or something

tidy data

a way of mapping the real world to a data set

observations

the things we are interested in, the rows, in an easy way it is all the first colums

attributes

pices of information, about the obserbations, that we are interested in, correspond to colums, all of the “data” on the top of the set, # of columns = # of attributes

measures

the way in which we ollect information about observations

quantitative data

data in which the values of an attribute are numbers representing a quantity of something, hint- decimals

categorical data

data in which the values of an attriute for an observation are selected from a set of different category labels

rating scale data

data in which the values of an attribute for an observation are selected from a predetermined list that has an order to it (strongly disagree, agree… OR scale from 1-10), rating scale has an OBVIOUS ORDER to it

text data

data in which the values of an attribute for an observation is text, typially from an open-ended question

time series data

data in which the values of an attribute for an observation indicate a moment in time, not how long something is- the MOMENT in time IT HAPPENED

RELIABILITY (memorize exact)

the extent to which the data you collect from a measure truly represents and reflects the real world characteristics of the observations

data validation

the act of ensuring that the values collected from each observation for each attribute are valid

data cleaning

removing invalid values from a dataset

univariate analysis

the analysis of a single attribute or variable at a time

standard deviation

the measure of spread, the typical amount by which each observation is different from the mean

five number summary

minimum, first quartile (25%), median, third quartile (75%), maximum

box plots

graphic depiction of a five number summary

mean

the average

median

the middle

dot plot

graph where each observation is displayed as one point on the graph

density plot

very similar to a dot plot with a line drawn across the top of all the stacks of dots

first quartile

25 percentile, the number at 25 means n had a “score” of x or LOWER

third quartile

75 percentile, the number at 75 means n had a “score” of x or LOWER

frequencies

total number of observations whose response is equal to a particular value, “how many”

relative frequencies

the percentage of all observations without missing values whose value is equal to a particular response, out of everyone, how many?

bar graph

based on a frequency table, has one bar for every response option, the bars height is equal to each response option’s frequency or relative frequency

word cloud

graphically depicts the words across the responses from the observations

distribution

the pattern that the responses from all the observations

normal distributions

bell curve, have a value near the average

unimodal distributions

distributions with only one peak

multimodal distributions

distributions with more than one peak

skewed distributions

normal distribution but with one of the side stretched out

right skew

pulled to the right, mode: closer to the left, median: closer to the right, mean: closest to the right

left skew

pulled to the left, mode: closer to right, median: closer to left, mean: closest to left

middle 95%

the distribution represents MOST of the observations

standard deviation

upper limit of middle 95%- lower limit of 95% / 4

two- way table

similar to a frequency table, except one attriute’s frequencies are presented as different rows in the table, and a second attribute’s frequencies are presented as columns`

column percents

relative frequencies based only on the total from a SINGLE column

absolute difference

two colons percents by SUBTRACTING one column percent from the other

absolute difference scale

0%- very similar, 5%- pretty similar, 10%- the SWITCH to different, 15%- VERY different

relative difference

two column percents by dividing one column from the other

relative difference scale

1.0- pretty similar, 0.8/1.25- slightly different, 0.6/1.5- very different

line graph

places time on the horizontal (x) axis, and the percentage on the vertical axis

grouped density plots

two density plots on the same graph

ratio of standard deviations

equal to the largest standard deviatio between the two groups divided by the smallest standard deviation, larger SD/ smaller SD

ratio of standard deviation scale

1.0- very similar, 2.0- pretty similar, 3.0- pretty different, 4.0 very different

effect size

equal to the mean difference divided by the larger standard deviation, group 1 mean - group 2 mean / larger SD

effect size scale

0.00- groups very similar, 0.25- pretty similar, 0.50- different, 0.75- very different, 1.00- extremely different

scatter plot

a plot in which each observation is placed as a point on a graph according to their value for each of the two quantative attributes

smoothed trend line

line through the average value of the vertical axis attribute across all values of the horixontal axis attribute

positive trend

trend line goes from the bottom left to the top right

negative trend

trend line goes from top left to bottom right

flat line

no trend

another word for slope is…

direction

another word for variability is…

strength

interaction plot

similifies comparing distributions between two sets of different groups by focusing just on the relative frequency or mean

interaction

difference in directions/ slope

margins of error

formal quantification of the uncertainty inherent to an inference

always prefer…

interval estimates over a single number of an estimate