Chapter 5 350 test 2

what type of graph do you use if the grouping variable is nominal or ordinal?(central tendency)

bar graph

what are the three types of frequency distribution graphs?

bar graph, histogram, frequency polygon

when the z score is negative that means the score is

below the mean

What is the mean?

"average"- add up all numbers and divide by number of numbers (n)

normal distribution/curve

"bell shaped," and symmetrical most scores should fill in the middle frequency gets lower as you get into the tails * with idealized or theoretical distribution graph should never touch the x axis Speed of automobiles at one spot on the highway Sizes of snowflakes Lifetimes of lightbulbs Errors in measurement (Galileo) Number of heads in a bunch of coin flips

What is the median?

"middle" value - numbers must be arranged from lowest to highest The score at the 50th percentile

inferential statistic

extends beyond your data

Where is the median lie in a skewed distribution?

Median lies in between the mean and the mode in a skewed distribution

what is simple frequency?

Simple frequency: The number of times each score f occurs in a set of data

Where is the mode lie in a skewed distribution?

Since mode is the most frequently occuring score, it lies in the hump of a skewed distribution

when the z score is positive that means the score is

above the mean

why are all scores (simple deviations) always equal to zero?

all scores above the mean are equal to the amount that below in a normal distribution

rectangular distr

all scores occur within the same frequency

what is the relative position of the measures of central tendency (mean median and mode) in a normal distribution?

all three measures should be identical

Inferential statistics

allow you to draw conclusions about a population using sample data

Frequency Polygon

also known as a line graph measures a large amount of interval or ratio data must include a score lower and higher than the range

as deviation increases what happens to frequency

as deviation increases the frequency decreases

when the z score is zero that means the score is

at the mean

what are the negatives of using mode as the central tendency?

Works for unimodal distributions Not so much for bimodal or rectangular Even if the data is unimodal, mode doesn't see skew It ignores all data except the most frequently occurring score

standard deviation

a computed measure of how much scores vary around the mean score the variance once it has been square rooted (square root of the variance)

a larger amount of variability in a data set is indicated by

a large range of numbers in a dataset ex: 89, 20, etc opposed to ex: 1234

what are the two main measures of variability?

range and standard deviation

what are the types of variability?

range-sensitive to extreme values and not anchored to mean variance SD-best way to measure because it is anchored to the mean and same units of simple deviations

platokertic distribution

too spread out sample// think platypus

what are the limitations of range?

- it is sensitive to really high and really low scores - it isn't anchored to the mean - use only with nominal or ordinal data or in combination with other measures for interval and ratio data

valence of deviations (+or -). In other words, what does it mean if the deviation is positive or negative?

- positive deviations= higher than the mean -negative deviations = lower than the mean

interpreting standard deviation (definition etc)

- the average amount that the scores deviate from the mean - will always be positive number (unlike simple deviation) - the larger the standard deviation, the more spread out the scores are

Frequency distribution:

A table or graph organizing data and displaying how often scores occur

what are the positives of using median as the central tendency?

1) easy to compute/ comprehend 2) not disordered by outliers/ skewed data 3) can be determined for ratio and interval scale Advantages of using the median instead of mode: ✴ only one score can be the median ✴ The median accounts for the frequency of all the scores (but not their values)

what are the steps for calculating standard deviation?

1) find n and the mean of scores (m or u) 2) find the simple deviations by subtracting the mean from each score 3) square the simple deviations 4) sum of squared deviations (SS) 5) for O (SD population) divide by n and take the square root for SD divide by n-1 and take the square root

what are the negatives of using median as the central tendency?

1) it does not take into account the precise value of each observation and hence does not use all information available in the data 2) unlike mean, median is not amendable (can not be extended) to further mathematical calculation and hence is not used in many statistical calculations

what are the positives of using mode as the central tendency?

1) only measure of central tendency that can be used to measure data in a nominal scale and ordinal 2) it can be calculated easily

what are the negatives of using mean as the central tendency?

1) sensitive to extreme values/ outliers, especially when the sample is small. (thats why its not appropriate for skewed distribution) 2) cannot calculate nominal/ordinal data

what are the positives of using mean as the central tendency?

1) uses every value in data and is hence a good representative of the data 2) the measure of central tendency that best resists the fluctuation between different samples (because repeated samples drawn from the same population tend to have similar means) 3) closely related to standard deviation, the most common measure of dispersion Only when the data is interval/ratio Most common method of finding the central tendency The mean best describes the data when the shape of the distribution is relatively normal

how do you start a frequency distribution table?

1. Put the score (X) column on the left and an f column on the right 2. Put the lowest score at the top of X column 3. List all whole-numbers between the lowest and highest score in increasing order. Do not skip numbers that do not occur! 4. If nominal, list out the groups (categories).

what is the percentage of scores that fall within one standard deviation of the mean?

68%

what is the percentage of scores that fall within two standard deviations of the mean in a normal distribution?

95%

what is the percentage of scores that fall within three standard deviations of the mean?

99.7%

ratio scale

A scale of measurement where values measure quality, and have order, equal intervals and a true zero Number value 0 is absolute Qualities of an interval scale plus has a true zero Distance, time, and weight For example, may define cell phone dependence by how long it is between phone calls (made and received) during a one-hour period. Mean median and mode can be calculated Number of years in college, reaction time asking people to write how many times they have been skydiving

what does central tendency do?

A score that summarizes the location of a distribution • what scores TEND to be • Most typical score

Ordinal scale

Category (in order) Rank in army Ordinal Scale is defined as a variable measurement scale used to simply depict the order of variables and not the difference between each of the variables. These scales are generally used to depict non-mathematical ideas such as frequency, satisfaction, happiness, a degree of pain etc. It is quite straightforward to remember the implementation of this scale as 'Ordinal' sounds similar to 'Order', which is exactly the purpose of this scale. How satisfied are you with service? (1= very satisfied, 5= not satisfied at all) Rank order your preference for the following foods from 1= most preferred to 4= least preferred A scale of measurement with numbers that have order so that each number is greater or less than other numbers but the interval between them is not equal also called rankings. asking people to assign a rank to a list of 10 breakfast foods in terms of how much they like the foods

interval scale

Interval Scale is defined as a numerical scale where the order of the variables is known as well as the difference between these variables. Variables which have familiar, constant and computable differences are classified using the Interval scale. It is easy to remember the primary role of this scale too, 'Interval' indicates 'distance between two entities', which is what Interval scale helps in achieving. Number value, equal space, 0 is not absolute What is your family income? What is the temperature in your city? A scale of measurement that has both order and equal intervals between values on the scale Likert type scale- a commonly used type of interval scale response in which items are rated on a range of numbers (usually between 5 and 7) that are assumed to have equal intervals Do not have true zero Temperature, how satisfied you are with a service ranging from 1=very dissatisfied to 5= very satisfied asking people to rate the extent to which they are happy with Marist on a scale of one (unhappy) to 7 (happy)

what are the limitations of range?

It is sensitive to really high/really low scores. ○ It isn't anchored to the mean. ○ Use only with nominal or ordinal data or in combination with other measures for interval and ratio data. Nominal/Ordinal data: The number of categories.

nominal scale

Nominal scale is a naming scale, where variables are simply "named" or labeled, with no specific order. Ordinal scale has all its variables in a specific order, beyond just naming them. Interval scale offers labels, order, as well as, a specific interval between each of its variable options. Ratio scale bears all the characteristics of an interval scale, in addition to that, it can also accommodate the value of "zero" on any of its variables. Nominal Scales: Nominal Scale, also called the categorical variable scale, is defined as a scale used for labeling variables into distinct classifications and doesn't involve a quantitative value or order. This scale is the simplest of the four variable measurement scales. Calculations done on these variables will be futile as there is no numerical value of the options. Foods I consume for lunch throughout a week (sandwiches, pasta, salad) Different shoes I wear in a week (sandals, flip flops, boots) A scale of measurement where numbers represent categories and have no numerical value Category, hair color, eye color, major asking people their favorite show on netflix

Distribution:

Positioning or arrangement

Where is the mean always pulled in a skewed distribution?

The mean is always pulled toward the extreme observations, so therefore it is shifted to the tail in a skewed distribution

as the spread of data increases what happens to the standard deviation?

The standard deviation increases

what is the center or the average

central tendency

as the distance from zero increases the frequency

decreases

what is range?

distance between the two most extreme scores in a distribution (highest score-lowest score) describes variability in data( with a number) ex: range =12-0=12 12 is the number to describe variability in data

whats the difference between graphing mean and graphing central tendency?

frequency is one variable while central tendency measures two variables a frequency graph uses a bar graph, histogram or a frequency polygraph and y axis is frequency graphing central tendency is only a bar (nominal or ordinal) or line graph (interval or ratio)

what do measures of variability communicate?

how spread out the scores are how similar the behaviors of the sample are how accurately the mean describes the distribution - more variability=less accuracy

how do we find percentiles

just add proportions to the left of z scores you are interested in and multiply by 100!

what type of graph do you use if the grouping variable is interval/radio? (central tendency)

line graph

if measurement scale of the dependent variable is interval/radio, what do you compute if the variable is normally distributed

mean

what is notation for mean and standard deviation in a population?

mean- u (mnu) standard deviation- O

what is notation for mean and standard deviation in a sample?

mean-M standard deviation=SD

Bar Graph

measures nominal or ordinal data- therefore shape does not matter because categories are random there is a vertical bar over each score type there are spaces between the bars frequency on y axis

if measurement scale of the dependent variable is interval/radio, what do you compute if the variable is not normally distributed

median

what are the different kinds of kurtosis of distribution?

mesokurtic, leptokurtic, platokurtic

negatively skewed

mostly high scores with a few low scores examples include exam scores, age of retirement

positively skewed

mostly low scores and a few high scores examples include company salaries, reaction times mileage of used cars

what are the different kinds of shapes of a frequency distribution?

normal distribution curve, negatively skewed, positively skewed, bimodal, retangular

mesokurtic distribution

normal distribution- having the average amount of spread

percentile

precent of total scores at or below that score (cf/n) x 100 cf= cumulative frequency: or number of scores at or below that score

precent

proportion of times a score occurs multiplied by 200 n= number of total scores (f/n) x 100

What is central tendency? Why is it important

provides a measure that attempts to describe a whole set of data with a single value that represents the middle or centre of distribution this is important because it tells us normal or average for a set of data it also condenses the dataset down to one representative value, which is useful when you are working with large amounts of data

scores in population vs sample

samples tend to have less variability than the parent population because extreme scores occur infrequently and are less likely to end up in a sample

what does the size of deviation indicate?

size of deviation indicates distance of each score from the mean -high number= further - in a normal distribution the greater the distribution the less frequent the score

Histogram

small amount of interval and ratio data no spaces in between the bars frequency on y axis

leptokurtic distribution

smaller/too thin distribution -think/ imagine tall leaping kangaroos

Descriptive statistics

summarize the data in front of you

bimodal distribution

symmetrical with two distinct humps, high and low scores with a few scores in the middle - two distinct humps -two distinct populations -height of men and women at marist

deviation from the mean (simple deviation)

the amount that a score in a sample differs from the mean of the sample; also called a deviation - each score in a dataset can be described as a deviation from the mean by subtracting the mean from the score (x-m)

variance

the deviation from the mean (x-m) squared, after it has been divided by n or n-1 in a sample (still under the square root sign)

if measurement scale of the dependent variable is ordinal/nominal, what do you compute

the mode

simple frequency

the number of times a score occurs in a data set

is the z distribution the same shape or different shape as the raw distribution?

the same shape as the raw distribution

why do we subtract n-1 in a sample?

the variability in a sample underestimates the variability in a population it comes from as you divide by a smaller number the answer is inflated AS n becomes larger, impact of n-1 becomes less improtant

what is a z-score?

the z score is a scores distance from the mean in standard deviation units also known as standard scores or "standardized scores"

what is the difference between graphing simple frequency and percentage?

there is no difference in shape, but the y axis must be capped at 100 y axis changes only, this is in order to accomodate we are now measuring percentage rather than frequency this is because the highest frequency terms will still have the highest percentile and therefore the spread will not change

why should we standardize your scores?

to understand position within a distribution FINISH

what does the type of graph depend on?

type of measurement

what is the mode?

value that occurs most often, if no number is repeated there is no mode

How do you determine which measure of central tendency to use?

which measure of central tendency you use depends on the measurement scale of the dependent variable (data)

how is frequency distribution graph set up?

y axis: frequency x axis: value range of all scores in sample

what does the sum of deviations always equal?

zero