Phycological Statistics Exam 1

Dr. Sestir Psych 2330

Descriptive Statistics

Describe data by simplifying it so it can be more easily understood or interpreted

Ex. ACT data

Inferential Statistics

Allows us to make inferences about larger groups through smaller subset data

Organizing info., communicating data effectively

Population

Parameter; entire group of people

Sample

Have the same characteristics as the population just on a smaller level

Random Samples

Everyone in a population has equal chances of being selected. Adds element of uncertainty

Nonrandom Samples

Specifically selected individuals based on non-random criteria rather than random

Constructs

Abstract idea that cannot be observed or measured directly

Operational

The exact procedures, actions, or measurements used to measure or manipulate a concept in a study

Independent Variable

IS MANIPULATED: IS THE CAUSE

Dependent Variable

BEING MEASURED: STAYS THE SAME

Extraneous Variable

ANY VARIABLE OUTSIDE INDEPENDENT THAT COULD ALTER DEPENDENT SCORES

Empirical Distribution

Based on evidence, what actually happened

Theoretical Distribution

Math model that shows how data SHOULD be distributed in the world

What is the Normal Curve?

Continuous, theoretical probability distribution that is perfectly symmetrical around its central peak

Why is the Normal Curve called Normal?

Bell shaped pattern occurs regularly in natural data

Why is the Normal Curve important to inferential stats procedures?

It allows researchers to draw accurate conclusions about entire populations using sample data.

Characteristics of a Normal Curve

Shape/symmetry, central tendency (MMM), Never touches 0, Continuous distribution

NOIR Scales

Use when need to deciding how to measure a variable and which statistical analyses are mathematically valid for data.

Discrete Scales

Ex. Number of siblings, Class rank, Marital status

Not good for histograms or bar graphs

Continuous Scales

Recognizing/defining/generating examples:

How does it affect graphs displaying data:

Measures of Central Tendency

Mean, Median, Mode

How to use:

How skew affects each:

Mode

Most common number in dataset

Not great descriptor

Median

Middle score from L-H; useful when dist. is highly skewed or has extreme outliers

Limits:

Mean

Average of all scores

Gives anchor point for variability

Measures of Variablitity

Tell us how spread out or clustered a data points are. CANT tell us individual values, shape of distb., etc.

Range

Lowest to highest value. Subtract lowest score from highest.

Interquartile Range (IQR)

Focuses on middle 50% of data.

IQR= Q³ - Q^1

Variance

Computation: find mean, find deviations, square deviations, sum squares, divide by degrees

• $$\sigma^2 = \frac{\sum (X - \mu)^2}{N}$$

Sum of Squares: multiply each deviation by itself

Properties: always non-negative; sensitive to outliers, scale, and units

Standard Deviation

Computation: find mean, find deviations, square each deviation, sum squares, calculate variance, take square root

• $$\sigma = \sqrt{\frac{\sum X^2 - \frac{(\sum X)^2}{N}}{N}}$$

Properties: measures in original units, non-negative, sensitive to outliers, changes, empirical rule

Grouped Frequency

Use for large range of data, continuous variables, too many individual scores, for data summarize

How to make frequency table: find range, determine intervals, calculate interval width, establish interval limits, count frequencies, verify total.

Ungrouped Frequency

Use for small range of data, discrete variables, few unique variables, exact score preservation

How to make frequency table: limit unique scores, tally scores, count frequencies, sum

Basics of Graphing

axes setup, title, labels, intervals

Difference in Bar Graphs and Histograms

bar graph is used for categories, bars don’t touch

histogram is used for continuous numbers, bars touch.

Frequency Polygons

What is it: graph that uses continuous line to show shape & trend of dataset

How to recognize & describe: jagged like mountain or trendline, many colors/lines/patterns, quickly analyzes data

Generating examples: test score distributions between 2 classes on 1 graph