Exam 1 Study Guide - Statistics

Chpt 1-5

Population

All individuals of interest for a PARTICULAR research question

Sample

A set of individuals from the population to PARTICIPATE/REPRESENT in the research study

Describe the relationship between a sample and a population.

The population → The sample is selected from the population → The sample → The results from the sample are generalized to the population

Statistic

value that describes a SAMPLE

Parameter

value that describes a POPULATION

Descriptive Statistics

Used to SUMMERIZE, ORGANIZE, and SIMPLIFY data

How is descriptive statistics helpful?

→ they take raw scores and summarize/organize them in a form that’s manageable

→ organized in table/graph to see entire set of scores

→ computes on average

Inferential Statistics

allows us to make statements about populations based on sample data

How are inferential statistics helpful?

→ they decide which interpretation is most reasonable

Sampling Error

the naturally occurring (by chance differences) discrepancy between a sample statistic and population parameter

→ differences occur by chance

→ sample statistics vary from sample to sample

→ don’t expect them to be equal, we expect them to be different

Operational Definition

defines a CONSTRUCT by identifying a procedure for measuring behaviors that can be observed.

→ hunger can be measured and defined by the number of hours since last eating

Why are operational definitions important?

→ they move from the abstract to the concrete

→ they measure frequency, duration, and intensity.

Discrete variables

SEPERATE; indivisible categories; NO VALUES exist between categories

→ for ex: flipping a coin or number of children in a household

Continuous variable

there are an INFINITE number of values; any two observed values

→ real limits

→ for ex: weight, height, temp., reaction time

Real limit

boundaries (upper/lower) of intervals for a score, halfway between adjacent categories

Nominal Scale

label/categorize; only labels differences that exist.

→ Mathematical operations - counting

→ Ex: Race, Gender, Marital Status

→ Political Affiliation and location of brain damage (no inherent order)

Ordinal Scale

label/categorize AND ORDER

→ Mathematical operations - rank order

→ Ex: Socioeconomic class and shirt size

→ Class rank and results of horse race

Interval Scale

label/categorize, order, and equal intervals

→ Mathematical operations - add and subtract

→ Ex: IQ and degrees F

→ test of verbal ability

Ratio Scale

label/categorize, order, equal intervals, AND ABSOLUTE ZERO

→ Mathematical operation - add, subtract, multiply, and divide

→ Ex: Kelvin, length, and weight

→ Annual income, number of errors made on an exam, time to complete a task

Correlational method

used to determine if there’s a relationship between the measured variables; used for prediction

→ no manipulation of variables

→ cannot demonstrate cause and effect

Ex: relationship or no relationship; strong or weak; positive or negative

Ex2: SCATTER PLOT; shows a clear relationship between Facebook time and academic performance

• as FB time increased, academic performance decreased

Experimental method (come back to this)

control and manipulation

→ Involves a comparison of the groups

→ can demonstrate cause and effect

→ consists of independent variable and dependent variable

Nonexperimental Methods (come back to)

→NO random assignment

→ compares pre-existing groups

→ pre-post test studies

• EX: Personality types (introvert vs. extrovert)

Independent Variable

MANIPULATED by experimenter

→ ex: types of study materials (digital vs. printed pages)

Dependent variable

MEASURED (observed) by the experimenter to asses the effect of the treatment

→ ex: GPA or class performance

Experimental Condition

DO receive experimental treatment

→ ex: anger management (new one)

Control Condition

DO NOT receive treatment

→ ex: anger management program (old one)

Extraneous variable

variables that effect the DV other than the IV

Participant variables

gender, body mass, personality, and intelligence

→ potential difference in our group

→ ex: number of math classes taken; this group is more conscientious than this group (personality)

Environmental variables

time of day, temp., noise, smell, and weather

→ ex: non-violent games during morning vs. violent games during night

Researcher control extraneous variables

1. random assignment

   1. each participant has an equal chance of being assigned to each of the treatment conditions

2. matching

   1. ensure groups are equivalent in terms of participant variables and environmental variables

3. using control variables

   1. study time and make it all the same so its not different between the two groups

Quasi independent variable

→ used to create the different groups of scores

Frequency Distribution

an organized tabulation of the number of scores located in each category on the scale of measurement

→ ordered from highest to lowest

What two elements are presented in a frequency distribution?

1. Categories (list all possible values)

2. Frequencies (number of operation set we see in a particular observation)

Why are frequency distributions helpful?

→ allows one to quickly see the data set and allows to see location of any individual score relative to all the other scores in the set.

proportion & percentage

• proportion

  • p = f/n

• percentage

  • p (100) = f/n (100)

Group frequency distribution

when you have a data set that covers a wide range of values

→ groups of scores instead of individual scores

Why would you want to use a grouped frequency distribution?

→ so the scores wouldn’t be long and cumbersome

→ to obtain a simple, organized pile of data (listing groups of scores into intervals)

What are class intervals?

1. there should be approximately 10 class intervals

2. the width of each class interval should be a simple number (2, 5, 10, 20, 50, 100)

3. the bottom score in each class interval should be a multiple of the width

4. All intervals should be the same width

What happens to the information in a set of scores when one moves from a frequency distribution to a grouped frequency distribution?

→ the cost of information is lost when categories are grouped

→ like you won’t know who specifically got what; the wider the interval, the more info we lose.

Histogram

→ height of the bar represents the frequency information

→ bars are adjacent to one another (no spaces)

→ no spaces because interval and ratio data have equal intervals

Modified/Informal Histograms

→ there is no y-axis

→ bar is replaced with blocks

→ each block represents frequency count

Polygon

→ replaced bar height with a dot above the particular category

→ height of that dot represents the frequency instead of the bar height

→ have a straight line between each adjacent category

→ no zero or seven category; you have to have one category beyond the last category and then go straight down to 0 from there.

Bar graph

→ there’s a space between each of the categories

→ no equal intervals

→ nominal: the space between emphasizes the scale consists of separate distinct categories

→ ordinal: separate bars are used because you cannot assume that the categories are all the same size!

Interval and Ratio scale

→ histogram and polygon

Nominal and Ordinal Scale

→ bar graphs

Symmetrical Distributions

→ if you put a line right down the middle, the right and left are mirror images of each other!

Positively skewed distribution

→ tail is on the RIGHT SIDE

Negatively skewed distribution

→ tail is on the LEFT SIDE

Central Tendency

a single score that defines/describes the center of distribution

Why do we have more than one measure of central tendency?

→ there’s not always one value that represents the group doing well

→ no single measure would accurately define the most representative so we have 3 methods

Mean

sum of ALL scores divided by the total number of scores

→ defines central tendency in terms of DISTANCE

→ balance point of distance

In what situation do you need to calculate a weighted mean?

→ when we need to calculate the mean of a COMBINED GROUP

Characterisicis of the mean

1. changing the VALUE of any score will change the mean

   1. numerator change not denominator

2. introducing a new score or removing a score will change the mean

   1. exception: if the score you add/remove is equal to the mean you started with, it won’t change.

3. adding/subtracting a constant from each score in the distribution will change the mean

   1. you add 2 to the score, you add 2 to the mean (same applied to #4)

4. multiplying/dividing each score by a constant will change the mean

Calculating the median

1. Order the scores of the distribution from highest to lowest

2. when there is an odd number of scores the median is the MIDDLE SCORE

3. when there is an even number of scores the median is the AVERAGE of the two middle scores

Mode

→ the score that occurs most often (the peak of frequency value) in a distribution.

• to find mode create a frequency distribution

  • advantage: can be used with any scale of measurement; MORE THAN ONE MODE

• Unimodal

• Bimodal

• Multimodal

  • major mode

  • minor mode

Median

the score that divides a distribution exactly in half

→ defines the of distribution in terms of number of scores

In what situations would you want to use the median instead of the mean? (come back)

1. when the distribution is skewed or has extreme scores

   1. the median gives us a better description of the center

2. when there are undetermined values

   1. if you’re working with people for a timed task (solving a puzzle), they might not finish in which they have a value that’s not a number, so you can still order from high to low,

3. the distribution is open ended

   1. can still order from low to high and calculate a median

4. using ordinal data

In what situations would the mode be a preferred and/or especially useful measure of central tendency?

1. when working with data on a nominal scale

   1. because mean and median can’t calculate something like political affiliation; you cannot add or rank them to find a mean or median.

2. when working with discrete variables

   1. people will use this when a fractional value is impossible for that particular score of measurement; number of children in a household.

3. when describing the shape of a distribution

   1. when a dataset has multiple distinct peaks or clusters (bimodal or multimodal), this highlights these separate subgroups or hidden trends that a mean or median would wash out.

Symmetrical Distributions

→ when you have a symmetric distribution, the median and mean are going to be IDENTICAL to one another.

What skewed distribution is this?

→ negatively skewed

→ mean closest to the tail

What skewed distribution is this?

→ positively skewed distribution

→ mean closest to the tail

Variability

a quantitative measure of the differences between scores in a distribution; a measure of the degree to which scores in a distribution are spread out or clustered together.

→ defined in terms of distance

What two purposes (the two discussed in class) does a measure of variability serve?

1. describes the SPREAD of distribution

   1. if small numbers are close together and large numbers are spread out

2. Tells us how well an individual or group of scores represents the distribution

   1. what are the odds that we can use that info to draw a conclusion about the population at large?

Range

the difference between the upper real limit of the LARGEST x value and the lower real limit of the SMALLEST x value

→ a measure of distance; the distance covered by the scores in a distribution

→ URL Xmax - LRL Xmin (15.5 - 3.5)

What is the problem with using range as a measure of variability?

→ the calculation only relies on the two extreme scores and it does not consider ALL of the scores in the distribution

when do you use population variance?

→ when your data set includes the entire group; every student in a small school

→ divides the SS by N and measures the exact spread of values for the whole group.

when do you use sample variance?

→ study a smaller group to estimate the traits of a LARGER population

→ divides by n - 1 because they tend to be LESS VARIABLE than their populations and this leads to a BIASED estimate of population variability.

Why is population variance computed differently than sample variance? How does the computational difference between population variance and sample variance deal with this issue?

→ when dividing n - 1, it’s just a correction for a problem that we have when we work with samples versus populations, as it increases the value which gives us a larger estimate

→ so n - 1 is a math procedure that we use to fix that problem in which samples tend to be less variable in the populations they represent and n - 1 makes us make a better guess.

Biased statistic

the average value for a sample statistic consistently underestimates or overestimates the population parameter

→ sample variance that uses n instead n - 1 as the denominator is a ___ statistic

→ the average value of the sample variance will consistently underestimate the population variance.

Unbiased statistic

the average value of the sample statistic is equal to the population parameter.

Standard Deviation

the typical distance between each score and the mean

Be able to describe the properties of standard deviation

1. adding a constant to each score in the distribution will NOT change the SD

   1. it doesn’t change the spread of scores it just moves it left to right

2. multiplying each score in the distribution WILL change the SD

   1. In the way that if you multiply every x by 2, you multiply the SD by 2