BILD 5 - Key Terms

Cognitive bias

Errors in thinking

- Overconfidence bias

- Confirmation bias

- Anchoring effect

- Overgeneralization

Confirmation bias

Seek out and process information that is consistent with existing beliefs

Anchoring effect

Reliance on first piece of information to make future decisions even if it is irrelevant

Model

Help us understand patterns in complex systems...See and communicate patterns by simplifying and removing noise

Statistics

Allow us to describe, understand, and predict without perfect information or guessing

Pilot data

Preliminary study (not in publication)

Hypothesis

- Clearly stated postulated description of how an experimental system works

- Proposed explanation for a phenomenon; not the absolute truth; assumption; potential "suspect"

- Testable, falsifiable, and specific

Null hypothesis

- The assumption of no pattern

- Combats human tendency to see patterns even when they don't exist

Alternative hypothesis

The hypothesis that states there is a difference between two or more sets of data

Scientific prediction

If [insert hypothesis] is false/not false, then I predict that my experiment will show [insert results of data analysis from experiment here]

Numeric data

Continuous, count, circular, ranked/scale is in the middle

Non-numeric data

Categorical, binomial

Missing values

NA or Null

Tidy data

1. Each variable forms a column

2. Each observation forms a row

3. Each type of observational unit forms a table

Scatterplots

relationship between 2 variables

Line graphs

relationship between 2 variables - 1 variable is ordered (usually time)

Histograms

distribution of 1 numerical variable (numerical value on x-axis)

Boxplots

distribution of 1 numerical variable

Barplots

comparing different categories (1 variable)

Violin plots

side-by-side comparison of multiple histograms

Heat maps

use color to show correlation

Statistical graphics

mapping of data variables to aesthetic attributes of geometric objects

Descriptive statistics

taking a dataset and calculating a set of summary measurements that simply communicate important (but incomplete) information

Mean

average

[X1 + X2 + ...Xn]/n

Median

the middle of all the ranked values

Mode

the most common value

Robust

an overall measure being resistant to single values

Anscombe's Quartet

four data sets that have nearly identical simple descriptive statistics, yet have very different distributions and appear very different when graphed

-Don't forget - Always plot!

Range

Xmax - Xmin = Range

IQR (interquartile range)

X75% - X25% = IQR

(Boxplots use IQR)

Variance

standard deviation squared

Standard Deviation

the square root of the variance (because same unit as data values)

Normal distribution

bell-shaped curve, symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean

Central Limit Theorem

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

Standard error of the mean

variability in sample means

- tells you how accurate your estimate of the real mean is likely to be

- true mean is unknown

- always true regardless of underlying distribution of data (CLT)

Standard deviation

variability in data points

- experimental mean is known

- only true if the population is normally distributed

95% confidence interval

There is a 95% chance that the true mean is within your 95% CI

- Sample mean +/- 1.96 the SEM

- +/- 1 SEM = CI of 68.26%

Parametric tests

powerful tests that see patterns from lots of assumptions

- Robust to non-normality

T test

ANOVA

Chi-squared

Homoscedasticity

Equal variance

Heteroscedasticity

Unequal variance

Skewness

measure of symmetry, or more precisely, the lack of symmetry

Kurtosis

measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution

- Platykurtic

- Leptokurtic

The Kolmogorov-Smirnov Test

Testing data for normality

- Compare our data to the ideal distribution

- Weak to data with many repeating values and weak to small sample sizes

The Shapiro-Wilks Test

- Weak to data with many repeating values and weak to small sample sizes

The D'Agostino's K-squared Test

Specific to the normal distribution. Complex but powerful

Error

- Data - model = error

- Error = random chance (stats) + bias (exp design)

Bias

Error that skews conclusions in a particular direction

Models

A set pattern based on prior knowledge and assumptions

Randomness

Error that does not skew conclusions in one direction or another

Objective

Research questions

Methods

Variables

Sample Size and Selection

Procedure

Statistical analysis