POLI30D (Live) Midterm 2 STUGU

z-score

Def: z score corresponds to a percentile or area under the curve; really is the percent observations to the left of the point denoted by the Z score

Formula: z = samplestat (xi) - mean / SD

not intepretable; refer to p-values

Standard error

Def: the standard deviation of the sample means; shows how much variation there might be between different samples of a population and the population

Formula: SE = mean / sqrt of the sample size

Confidence Intervals

def: propbabillity that a parameter will fall between a set of values

Importance; correspond to different z scores and p values depending on the confidence interval

• 90% confidence → 1.64 z score (.1: 2 tailed p value

• 95% → 1,96 z score (.05: 2 tailed p value)

• 99% → 2.58 z score (.01: 2 tailed p value)
  
  

Percentiles

A percentile indicates the percentage of a dataset that falls at or below a specific value.

idk its important to where the z score values land

Null Hypothesis (Ho)

Def: The assertion that any apparent difference you see in your sample does not reflect any real difference but is merely the result of probability

Importance: it provides a baseline assumption that any observed effect in an experiment is simply due to chance.

EX: there is NO difference between the mean of the feeling thermometer score for Obama for women and the mean feeling thermometer score for Obama for men

Alternative Hypothesis

Def: The assertion that there really is some real difference in your sample over and above whatever is attributed to random fluctuations

Importance: It represents the presence of an effect; can help disprove the null and give direction to true findings

Ex: There IS a difference between the mean FT score for Obama for women and the mean FT score for Obama for men

Statistical Significance

Def: the conclusion that random fluctuations alone can’t account for the size of the effect you observe in your data so the Null is likely false

Importance: allows us to confidently make decisions or rejections of hypotheses that are being tested

Ex: if a p value of a study that measures a relationship there is between two variables is less than .05 (a 95% confidence level) we can confidently reject that hypothesis and assume that it would not be statistically significant

Type i error

Def: False Positive error (??)

Importance: false positives can be damaging as you can act on something that isn’t true and then act in misconduct
Ex: if there is a type1 error in some Dr saying your arm is broken (when it’s not) and then they operate on it, it may make it worse

Type ii error

Def: false negative
Importance: still an error that can be made and shouldn’t be made, but can
Ex: if a Dr says that someone’s arm is NOT broken, and they don’t operate on it, it can still be fixed later although some more slight complications. Overall better than a type 1 because eventually you will circle back

type iii error

Def: when you arrive at the right answer to the wrong question

Importance: bro idk another way to avoid erroneous interpretations and conclusions about data

Ex: Because of poor study design or a flawed hypothesis (answering the wrong question), your study concludes the drug lowers blood pressure because of its unique chemical flavor, when in reality it only works by acting as a diuretic. You got the "right answer" (the drug works), but for the "wrong reason"

type iv error

Def: you arrive at the right answer but proceed to interpret it incorrectly

Importance: another error that can be made and avoided with proper precaution. Wrong interpretation may have a butterfly effect for those who come after

Ex: Dr correctly identifies that your elbow is broken, but suggests a bandaid or knee surgery will fix it

descriptive statistics

Def: Numerical data used to measure and describe characteristics of groups. Includes measures of central tendency and measures of variations

Importance: transforms raw, complex datasets into concise, easily interpretable summaries

Ex: mean data of 500

inferential statistics

Def: used to make predictions, generalizations, or conclusions about a larger population based on a smaller representative sample of data

Importance: allows us to attempt to infer and make generalizations about populations without gathering literally the entire population

EX: we want to draw a conclusion about ALL voters in California so we use a sample of a smaller group from which we collect data from and then infer further from

Independent t-test

Def: this test compares means between two samples where the selection of one sample does not effect the selection of the other
Ex: measuring the relationship between means between two samples

treatment group

Def: group in an experiment that is given the intervention/treatment/change that is being tested for

Importance: idk bro allows us to differentiate between the two groups

Ex: your treatment group is administered the medicine being tested, while the control is potentially given a placebo

control group

Def: group not given any specific intervention or treatment

Importance: allows us to refer back to unaffected people as a baseline

Ex: group that is not given a dosage of medicine

Restriction

Def: (A way to avoid issues while designing studies) Limit participation in the study who are homogeneous with regard to potential confound; restricting your study to something a bit more easy to measure

Importance: allows a more homogenous/easier group easier to measure to then limit confounds we may be worried about

ex: research in one country may be a lot easier than global research with a lot of different confounds

Randomization

Def: Randomly allocate participants to exposure groups so that the distribution of measured and unmeasured potential confounds should be equal across groups

Importance: allows us to avoid bias more; no extra steps of convincing

Ex: names out of a hat

Double Blinding

Def: eliminates bias because both investigators and participants are blinded to wether they are in the treatment or control group

Importance: reduces bias even further

Ex: a Dr randomly gives out a new pill they are testing out to participants, but doesn’t know which are the real treatment and which are a placebo

Triangularization

Def: Collecting data from various sources
Importance: helps increase validity or rule out alternative explanations
Ex: Stout research! We are triangularization by reviewing past literature, using an experiment, collecting data, and other ways to prove out conclusions

stratification

examine the observed associations by strata of the third variable to determine whether it is causing confounding of effect moderation

Multivariable analysis

use stats to adjust measures of association for potential confounds. This method allows for adjustment of multiple confounds at once

Experimental Morality

Def: a threat to experiments: Subjects leave the experiment non-randomly

Importance: if multiple subjects leave your experiment that could reveal some kind of issue/design flaw

Ex: you’re testing a medicine but then half the participants leave because they find the product unethical

Hawthorne Effect

Def: behavior by participant is altered because they are aware that their actions are being observed
Import: threat to validity

Ex: Someone temporarily modifies their behavior—often improving their performance because they know they are being observed

History

Def: You can’t PERFECTLY replicate an experiment as you can never go back in time; the history will always alter it

Importance: technically a threat to validity

Ex: can’t go back in time and give new tools to a rural village to see how they advance; that is set in stone and you are forced to experiment with another similar rural village instead

Instrumentation

Def: The measurement itself changes over time
Importance: threat to validity
Ex: IQ measurement standards have changed over time; may effect results

Maturation

Def: a confounding variable in research where natural developmental changes or the passage of time distort the results of an experiment.
Import: threat to validity; but also helps researchers isolate natural changes when researching
Ex: a study testing a new method to teach babies language, researchers notice babies talking significantly more after a year. However, this improvement is due to natural maturation and age, not the specific teaching method.

Selection Effect

Def: some aspect of selection affects outcome
Importance: threat to validity that is systematic
Ex: (volunteer bias, only sick receiving medicine)

Spillover

Def: when the treatment effects the control group indirectly

Import: threat to validity

EX: people getting vaccinated affects non-vaccinated community members

Test Sensitization

Def: the very act of measuring the cases (when preforming a pre-test) changes the cases;
Import: threat to test validity
Ex: asking a question about your opinion on Disney; you may get a very different answer if you asked political party first

Aggregate Fallacy

Def: erroneously inferring individual behavior from aggregations of individuals ; the logical and statistical error of assuming that trends observed at a group, population, or aggregate level automatically apply to the individuals within that group.

Importance: threatens interpretive validity

EX: a graph shows that the black population in states are voting for segregationist candidate, Wallace, in 1968. Upon further review, it shows that white voters had greater turnout in states with high black populations because they were more concerned with the increasing black civil rights → we had assumed originally that

Simpson’s Paradox

Def: when a lurking variable changes the direction of a relationship viewed between two other variables; put a bunch of variables together, but the second you factor out a confound, that trend could reverse

Contingency Tables

Chi-Square

Chi squared is used to measure the association for nomial and ordinal data

it tests to see whether distributions of categorical variables differ from each other

used to determine whether there is a statistically significant differnece between the expected frequencies and the observed frequences in one or more categories

Test of independence — are two categorical variables related? ("Is political affiliation independent of education level?")

x²= Sum of [ (Fo - Fe)² / Fe (just know how to find expected values with across down diagonal

Degrees of Freedom

df = (nrow-1)(ncol-1) (DONT USE TOTAL ROWS OR COLUMNS)

Observed Freedom

Expected Frequence

Statistical Independence

Lambda

Def: a measure of association used for nomial (categorical) data that determines how well an independent variable predicts a dependent variable

Import: reduces production errors/can help predict

Ex: you want to know if being male influences your preference for dogs or cats

Accord

Def: when Lambda = 0, it is called an accord; a type of association between two variables where percentages on the dependent variables can vary across independent variable categories as long as the

simple: X² can have a nonzero value even if Lamba=0

Regression

Bivariate Regression

Multivariate Regression

ŷ= β0 + β1x

Line of Best Fit

Slope

R-squared

Def:Effectively, R² is a measure of the goodness of fit of a model
close to 1 it is, the close fit the data is to the line of best fit, the closer to 0 the more spread the data is

import: allows us to visualize and see trends

Interpretation ex with R² = .234: Reading books within the last year explains 23.4% of the variance of high school students’s SAT reading scores; would be a relatively spread out data set

Intercept

Coefficient

Independent Variable

Def: The explanatory variable; the factor believed to cause or explain changes in an outcome. It is manipulated and observed to see its effect

Import: without identifying the IV we cannot trace what causes the DV. Fundamental to creating relationships

Ex: In studying for if being older makes you vote for Trump, being older is the independent variable that then would potentially affect the DV

Dependent Variable

Def: the outcome variable, what we are trying to explain or predict. Depends on the IV

Import: the DV is what we are measuring, it determines if the IV had any effect

Ex: In studying for if being older makes you vote for Trump, your vote for trump likelihood is the DV

Control Variables

Def: any factor or element in a study or experiment that is intentionally held constant

Import: isolates the relationship between your independent and dependent variables

ex: type of plant, amount of sunlight, type of soil, and pot size