Descriptive Statistics

Descriptive Statistics

Summarize/report general data

Inferential Statistics

Draws conclusions from data that have random variation

Research Process

1. Make a question

2. Research theories

3. Make hypothesis, prediction

4. Identify variable and measure

5. Analyze data

6. Generalize data

Population

Complete set of events interested in

Parameter

Numerical value summarizing population data

Sample

Set of observations of subset of population

Statistic

Numerical value summarizing sample data

Random Sampling

Every member of population has equal chance on inclusion

WEIRD

Western, Educated, Industrialized, Rich, Democratic

Sampling Variation

The statistics measure can vary from different samples, based on who you choose

Variable

Property of an object/event that can take on different values

Factors

IV, have an effect on the DV

Scores

Measurements/values, both DV and IV must be with measurement scales

Nominal

Classify by labelling items for qualitative data, no stats can be performed

Ordinal

Uses numbers to give items a ranked order so each get a property of magnitude but not equal intervals or tells difference between points

Interval

Numbers indicate order and absolute intervals between are meaningful because no rational 0

Ratio

Numbers indicate order, have interval, meaningful

Discrete/Categorical

Takes a set of possible values, nominal values are always discrete

Frequency Graphs

Visualize data to show frequency of how often a value appears in the measurement using only DV

Ceiling Effect

Data has cutoff, or clustered near the top

Bistable Perception

Brain perceives ambiguous stimuli as exclusive interpretations

Ceiling Round

Round up to nearest whole number

Modality

Number of peaks in data

Causes for Bimodal Distribution

Sexual dimorphism, ages, contamination

Skew

How asymmetrical an unimodal distribution is about peak

NegativeSkew

More distribution is to a smaller value

Positive Skew

More distribution is to larger value

Kurtosis

How tails of unimodal distribution are aorund the peak

Positive Kurtosis/Leptokurtic

More clustering near the average

Negative Kurtosis/Platykurtic

More variation of data

Proportion

Relative frequency based on the total of number of observations (put in decimals)

Mode

• Shows values in data, works on nominal data

• Can change based on how bins are divided

Median

• Not affected by extremes

• Can’t perform statistics, not very stable

Mean

Can be biased and values may not exist in data

Quartiles

Dividing data into four sections evenly

Interquartile Range

Describe range of the middle 50% distribution

Trimmed Statistics

Data with removed parts

Box and Whisker Plots

Displays Q1,Q2,Q3 as boxes, using the IQR as error bars

Drawing Box and Whisker Plots

1. Draw a line as median

2. Draw Q1, Q3 to create a box around the median

3. Multiply IQR by 1.5 and subtract bounds by that value to find a value no more than it as the error bars

4. Draw asterisks to show outliers

Violin Plots

Combines box plot with kernel density plot to show summary statistics with probability density of continuous numerical data

Variance

Subtracting data point from the mean, then averaging it

Variance Equation

Standard Deviation

Ȳ

Mean of sample

μ

Mean of population

σ

Standard deviation of population

Population Parameter

Everything is measured, average isn’t estimated therefore no dfs

Sample Statistics

Ȳ estimate, therefore dfs for further calculations

Z Scores

Transforming data into standardized z scores

Positive Z Scores

Observation is above the mean

Negative Z Scores

Observation below the mean

Floor Effects

Data is clustered near the bottom because test too hard

Regression

How the typical value of DV changes when IV changes

Covairance

Degree that 2 variables vary together

Correlation Coefficient

Standardizes covariance

r = 1

X and Y are perfectly correlated

r = 0

No relationship

r = 0.1-0.3

Weak correlation

r = 0.3-0.5

Moderate correlation

r = >0.5

Strong correlation

Curvilinear

Best fit line isn’t straight

Monotonic

As x increases, y increases or decreases

Nonmonotonic

As x increase, Y reverses once or more

r_s

For ranked/ordinal variables to tell how monotonic the relationship is

r_pb

For dichotomous and continuous variable

r_phi

For dichotomous variables

Factors Affecting Correlation

• Range restrictions

• Heterogenous samples

• Non linear data

• Extreme observations

Range Restrictions

Some cases must have areas restricted

Heterogenous Samples

Data which sample of observations could be divided into distinct set based on variable

Non linear data can have

The same r

Correlation

Shows relations to another casual factor, that can change over time or a coincidence

Regression

How typical value of dependent value when independent chances (best fit line)

Interpolation

Estimating something in data range but not on measured

Extrapolation

Estimating beyond data range

Residual

Difference between data and model line

Least Squares Regression

Line of best fit that minimizes the sum of the squared

SS_residuals

How good model fit is with a better model getting a smaller SS

SS_total

Measuring fit to a mean line

R²

Percentage thar variation of Y is accounted by X

If SS_r < SS_t

R² = 1, linear model fits better than mean

If SS_r > SS_t

R² = 0, linear not better than mean

R² = 1

Explains all variation

Multiple Regression

The dependent value may be correlated with many independent values, by applying many linear regressions, it quantify strength between DV and certain IV

Event

Outcome of an experiment

Probability

Ratio of occurrence of the specific event to all occurrence of events

Analytic View

Investigating trends, patterns with data

Frequentist View

Long run frequency of an event happening over repeated trials

Subjectivist Probability

Represents subject’s belief in likelihood of an event

Joint Probability

A and B happen in an experiment p(A∩B)

Union of Events

A or B happen in an experiment, p(AUB), both can’t be true

p(AIB)

Conditional probability

Statistical Independence

Occurrence of an event has no effect on the probability of another

Mutual Exclusion

Event A and B can’t happen at the same time, p(AIB) = 0

Risk

Chance of something based on all possible outcomes

Odds

Chance of something based on outcome not occurring

Odds Ratio

Comparison of events to each other

Odds = 1

Same odds for both scenarios

Greater than 1 Odds

A number times the numerator odds

OR < 1

Placebo has a stronger effect

OR > 1

Treatment has a stronger effect