PRELIM | Psychological Statistics (PSM102)

Statistics

a range of techniques and procedures for analyzing, interpreting, displaying, and making decisions based on data

Statistics is the language of ____ and _____

science and data

Statistics

serves as the link between a research idea and and usable conclusions

Statistics

provides tools that you need in order to react intelligently to information you hear or read

Statistics

can be used to add credibility to an argument or advice

Data

represent the measured value of variables

Variable

a characteristic or feature of the thing we are interested in understanding

Independent Variable

manipulated by an experimenter

Dependent Variable

shows the results after the independent variable is manipulated

Experimental Group

group that received the variable being tested in an experiment

Control Group

the group in an experiment that does not receive the variable you are testing

Qualitative

express a qualitative attribute such as hair color, eye color, religion, favorite movie, gender, and so on. The values do not imply a numerical ordering.

Quantitative

measured in terms of numbers. Some examples are height, weight, and shoe size.

Discrete

variable you can count in a finite amount of time

Discrete

countable, instead of measurable

Discrete

easy to visualize and distribute, and can be categorical

Continuous

can assume an infinite number of real values within a given interval

Continuous

variable that changes over time, may or may not have decimals, and visualized with line graphs or skews

Nominal

naming or categorizing responses

Ordinal

uses labels to classify cases (measurements) into ordered classes

Interval

there is order, the difference between the two variables is meaningful and and equal, and the presence of zero is arbitrary

Ratio

the most informative scale and an interval scale with the additional property that its zero position indicates the absence of the quantity being measured

Sample

a small subset of a larger set of data

Population

the larger set from which the sample is drawn

n

sample

N

population

Simple Random Sampling

most straightforward among the sampling strategies

Simple Random Sampling

requires every member of the population to have an equal chance of being selected into the sample

Simple Random Sampling

the selection of one member must be independent of the selection of every other member. picking one member from the population must not increase or decrease the probability of picking any other member (relative to the others)

Stratified Random Sampling

sometimes used to make the sample more representative of the population since simple random sampling often does not ensure a representative sample

Stratified Random Sampling

this method can be used if the population has a number of distinct “strata” or groups

Convenience Sampling

a non-probability sampling method where units are selected for inclusion in the sample because they are the easiest for the researcher to access

Convenience Sampling

can be due to geographical proximity, availability at a given time, or willingness to participate in the research

Sampling Bias

occurs when some members of a population are systematically more likely to be selected in a sample than others

Sampling Error

a deviation in the sampled value versus the true population value. occurs because the sample is not a representative of the population or is biased in some way

Experimental Research Design

• defined by the use of random assignment to treatment

• conditions and manipulation of the independent variable

Quasi-Experimental Research Design

involves manipulating the independent variable but not randomly assigning people to groups

Non-Experimental Research Design

sometimes called Correlational Research

Non-Experimental Research Design

involves observing things as they occur naturally and recording our observations as data

Types of Statistical Analyses

Descriptive Statistics & Inferential Statistics

Descriptive Statistics

numbers that are used to summarize and describe data. data refers to the the information that has been collected from an experiment, survey, historical record, etc.

Inferential Statistics

the formal analyses and tests we run to make conclusions about our data

Inferential Statistics

use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects

X and Y

variables being observed in an experiment or research

Σ

indicates summation

i = 1

indicates that the summation is to start with x₁

4

indicates that the summation will end at x₄

Frequency Distribution

an organized tabulation showing exactly how many individuals are located in each category on the scale of measurement

Frequency Tables

shows the frequencies of the various response categories and the relative frequencies, which are proportion of responses in each category

Regular Frequency Distribution

When a frequency distribution table lists all of the individual categories (x values), it is called _________

Class Intervals

groups of scores

Grouped Frequency Distribution

In a grouped table, the x column lists groups of scores, rather than individual values

the same width

In grouped frequency distribution, the intervals all have _________, usually a simple number such as 2, 5, 10, and so on

Multiple

Each interval begins with a value that is a ________ of the interval width

Interval Width

selected so that the table will have approximately ten intervals

Cumulative Frequency

Calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. The last value will always be equal to the total for all observations, since all frequencies will already have been added to the previous total.

Relative Frequency

A proportion or percentage which is calculated with the help of given frequency

f/N

formula of relative frequency

1

total of relative frequency

Interpolation

mathematical process based on the assumption that the scores and the percentages change in a regular, linear fashion as you move through an interval from one end to the other

Percentile

commonly expressed as the percentage of values in a set of data scores that fall below a given value

n/N * 100%

formula for percentileQya

Quartile

three values that split sorted data into four parts, each with an equal number of observations

Decile

each of ten equal groups into which a population can be divided according to the distribution of values of a particular variable

Pie Chart

each category is represented by a slide of the pie and the area of the slice is proportional to the percentage of responses in the category

Pie Chart

This is simply the relative frequency multiplied by 100

Pie Chart

effective for displaying the relative frequencies of a small number of categories but not recommended when you have a large number of categories

y-axis

In bar charts/graphs, this is where frequencies are shown

x-axis

In bar charts/graphs, this is where the variable is shown

Bar Charts/Graphs

Typically, the y-axis shows the number of observations in each category rather than the percentage of observations in each category as is typical in pie charts

Lie Factor

refer to the ration of the size of the effect shown in a graph to the size of the effect shown in the data

Baseline in bar charts/graphs

the bottom of the y-axis, representing the least number of cases that could have occurred in a category. Normally, but not always, this number should be zero

Pie Charts and Bar Charts/Graphs

can be used for graphing qualitative variables

Line Graph

essentially a bar graph with the tops of the bars represented by points joined by lines (the rest of the bar is suppressed)

Line Graph

generally better at comparing changes over time

Stem-and-Leaf Display

graphical method of displaying data. It is particularly useful when your data are not too numerous

Stem-and-Leaf Display

Its one purpose is to clarify the shape of the distribution

Histogram

graph that shows the frequency of numerical data using rectangles

distribution frequency of a variable

In Histogram, this is what the height of a rectangle (the vertical axis) represents

Frequency Polygon

A curve that is drawn on the x-axis and the y-axis

Frequency Polygon

can serve as an alternative to a histogram

x-axis

In frequency polygon, it represents the values in the dataset

y-axis

In frequency polygon, it shows the number of occurrences of each distinct category

x-axis

where the frequency polygon needs to start and end

Frequency Polygon

the points in this graph represent frequency of values within a particular interval rather than actual data value.

Box and Whisker Plot

Otherwise known as a boxplot, is a graph summarizing a set of data

Box and Whisker Plot

shows how the data is distributed and it also shows any outliers and a useful way to compare different sets of data

Bar Graph

This graph should be used when the score categories (x values) are measurements from a nominal or an ordinal scale

Bar Graph

This graph is just like a histogram except that gaps or spaces are left between adjacent bars

Line Graph, Stem-and-Leaf Display, Histogram, Frequency Polygon, Box and Whisker Plot, Bar Graph

can be used for graphing quantitative variables

Bell Curve

a common type of distribution for a variable, also known as the normal distribution

Bell Curve

originates from the fact that the graph used to depict a normal distribution consists of a symmetrical bell-shaped curve

Skew

most common asymmetry; one of the two tails of the distribution is disproportionately longer than the other

Skew

This property can affect the value of the averages we use in our analyses and make them an inaccurate representation of our data, which causes many problems

Skew

can either be positive or negative (also known as right or left, respectively), based on which tail is longer

Positive Skew

Negative Skew

Arithmetic Mean

the sum of the numbers divided by the number of numbers

μ

mean of a population

M or x̅

mean of a sample