PsychStats Exam 1 (Weeks 1-4; Descriptive Statistics)

Population of Interest

the larger group the researcher actually wants to draw conclusions about

Sample

the subset of that population who actually participate in your study

Independent Variable

the input

Dependent Variable

the outcome

Operational Definition

the exact way you will measure or manipulate that variable

Nominal

unordered categories

Ordinal

ordered categories (unequal gaps)

Scale

numbers with real mathematical meaning

includes interval and ratio

Interval

scale measurements without a meaningful 0

(ex. temperature or SAT scores)

Ratio

scale measurements with a meaningful 0

(ex. height/weight, income)

True Experiment

IV manipulation + random assignment = causal claim

Quasi-Experiment/Correlational

No IV manipulation + naturally occurring groups = no causal claim

Descriptive Statistics

summary of the data from a specific sample

(ex. histographs, bar graphs, box plots)

(ex. mean, median, mode)

(ex. range, IQR, standard deviation)

Inferential Statistics

sample —> population

chance and probability

null hypothesis significance testing

Raw Data

data distributions where every individual score is visible

(ex. frequency table, histogram, scatterplot)

Aggregated Data

individual scores collapsed into summaries

(ex. bar graphs, line graphs)

Histogram vs. Bar Graph

histogram = raw data, no gaps, scale

bar graph = every bar is a group mean, have gaps between them, nominal/ordinal

Bimodal/Multimodal Distribution

two or more peaks

(often a sign of two different groups mixed together)

What’s special about mode?

it’s the only one (not mean or median) that can work for nominal data)

An outlier would affect what the most?

mean—an outlier barely moves the median but the outlier will drag the mean toward it

What happens when you add the deviations above and below the mean together?

they cancel each other out (assuming the mean is the middle)

Why do we square the standard deviation?

to prevent the upper and lower halves of the mean from cancelling each other out

creating only positive numbers to do math with

How does a skewed graph affect the mean more than the median in a symmetrical graph?

the mean has to move farther toward the tail to compensate while the median only moves one over

When is the median a better summary than the mean?

nominal/ordinal, bimodal/multimodal, open-ended intervals, skewed distributions, and data with strong outliers

When is the mode a better summary than the mean?

nominal data

Range

highest - lowest

however, a single outlier defines it entirely

Interquartile Range (IQR)

72th percentile - 25th percentile

ignores the extremes

Standard Deviation

the typical distance a score falls from the mean

uses every score in the dataset

SD Formula

Each scores deviation from the mean —> square them —> average the square —> square root

Z Score (definition)

how many standard deviations is this score away from the mean, and in which direction?

Z Score (formula)

[raw score - mean] / standard deviation

What counts as an outlier?

anything beyond 3 standard deviations (either direction)

When do z scores and percentiles count?

z scores - always

Percentiles - ONLY on normal curves!!

Samping Error

the error that occurs whenever we use a sample to estimate a population

Law of Large Numbers

a sample tends to mimic the underlying population more and more closely as the sample gets larger and larger

aka less sampling error

Null Hypothesis

there is no effect of IV on DV. any result is a sampling error

Alternative Hypothesis

there is an effect of IV on DV. The difference is real

Four-Step Logic to Test Null Hypothesis

1. set an expectation

2. run the study

3. locate that value

4. judge it

Writing in APA style:

round to 2 decimals

avoid passive voice (we or I is fine)

Italicize symbols

Null Hypothesis

the “nothing happened” assumption

Alternative Hypothesis

the “something happened” suprirse/unusual result

Population Mean

the average of an entire group of data

Sample Mean

the average of just a small subset taken from that group

Point Estimates

calculated value as a “best guess” to estimate an unknown population parameter (ex. mean, SD, etc)

find the mean of the confidence interval values

Parameter

a fixed numerical value that describes a characteristic of an entire population

Confidence Intervals

express a range of possible values for the population mean

constructed by finding the sample mean and building an interval around it

Practical Significance

measures whether a research result or data effect has real-world value

Cohen’s D

the effect size of the difference between two group means

0,2 = small

0.5 = medium

0.8 = large

Central Tendency values

mean, median, and mode

Variability/Dispersion

range, interquartile range, and standard deviation

Descriptive Stats

summarize the sample and allow inferences about the underlying population

Inferential Stats

characterize how extreme/odd the study results are if nothing actually happened (no effect of IV on DV)

T-test

a statistical test used to determine if there is a significant difference between the means of two groups

The more different the sample means are, the [] likely it is they were drawn from populations w/ the same mean

less

P-value

a number between 0-1 that measures the likelihood of getting extreme results if the null hypothesis is true

< or = 0.0 is statistically significant

>0.05 is probably random chance (not significant)