Exam 3 Flashcards
What is an appropriate measure to summarize ordinal data
Median
When a line graph is employed to represent the number of subjects who received each possible score on a variable, this graph is called a frequency ____\
Polygon
What is the difference between descriptive and inferential statistics?
Descriptive statistics summarize data
Inferential statistics determine the probability that results are due to chance
If you were to graph the results of tatste test between two different types of beverages, the type of beverage w hod appear on the
Horizontal axis
What would be an appropriate measure of centeral tendency to summarize interval data
Mean median and mode
In a _____ a separate and distinct _____is drawn to represent the number of people who received a possible score
Bar graph
Bar
The standard deviation would be an appropriate measure of variability only if the variable is measured on a _____ scale
Interval
In a survey examining the number of third vs 6th grade students who buy their lunch at school, the most appropriate description of the results would be to
Compare group percentages
A researcher wants to graph the results of a study that examined of food consumption affected preference for a movie. In This example, the preference for the movie should appear ___\
On the vertical axis
Example of histograms or frequency polygons
“clustered column” (Excel) or line graphs
Sampling error
When you only have a sample and not the entire population. This can result in skewed values
Statistic vs parameter
Statistic- characteristic of a small part of the population, i.e. sample.
parameter-fixed measure which describes the target population.
The statistic is a variable and known number which depend on the sample of the population while the parameter is a fixed and unknown numerical value.
Descriptive statistics
uses the data to provide descriptions of the population, either through nu
Inferential statistics
makes inferences and predictions about a population based on a sample of data taken from the population in question.
3 characteristics that completely describe a distribution:
Shape, central tendency & variability
Normal distribution shape
Symmetrical. Bell curve
Histogram/frequency polygon chart shape
Skewedness. Can be positive to negative
Frequency distribution
Shows number of instances in which a variable takes each of its possible values.
Central Tendency
– It is the score that indicates where on the scale the distribution is located
– It indicates the value of the variable around which most of the scores are found.
– A measure of central tendency is usually (but not always) near the center of the distribution.
Population
μ, N
Sample
n
_
X(or M)
Mode
Score that shows the most
Can be used on all for scales of measurement measurement (nominal, ordinal, interval, ratio)
Only one that can be used for nominal dependent variables
What is the only central tendency that can be used for nominal dependent variables
Mode
What can be used on all four scales of measurement
Mode
How do bar graphs differ from line graphs or histograms
Line graphs and histograms do not show frequency distribution
Histograms and line graphs are used for ratio and interval data
Median
The median is the score below which half of the scores in the distribution fall; it is the 50th percentile
“I make less money than average, but (almost) more money than most.
What am I?”
The median
When can the median be used
ordinal, interval, ratio
When is the median most useful
When describing skewed data
In highly skewed data, the _____most accurately reflects the center of the scores.
Median
Problems with the Median
it is based on counts of scores, not on the value of the scores.
mean
Average score located at the exact mathematical center of a distribution
Limitations of the Mean
Since the mean requires variables with equal intervals it can only be used on interval or ratio scales of measurement
extremely sensitive to extreme scores
What central tendency method can only be used for interval or ratio data
The mean
What are most inferential statistics based off of
The mean
Variability
How different or spread out scores are in a distribution
Ways to measure variability
Range
Sum/average of deviations
Sum/average of deviations squared
Variance (population & sample)
Standard deviation (population & sample)
Range
The simplest, and least informative, measure of variability
Range = Highest Score – Lowest Score
Problems with the range
Two different sets of numbers can have the same range, even though they are very different.
It does not take into account all of the information that is available in the entire set of scores.
When is the Range used?
In descriptive manners.
Ex-describing age. The age ranged from 14-77
Problems with Deviations from
the Mean. What to do about it
Average of the deviations always equals zero
What to do about it - The sum of squared deviations from the mean” or “Sum of Squares” (SS)
Deviation from the mean
X-average
Formulas for variance
“definitional” or “derivational”
“computational” or “raw score”
“calculational”(book)
Problem with variance
Variance is unrealistically large, and is interpreted in squared units
– To get back to regular or “standard” units we take the square root after calculating the average squared deviation score (aka, variance)
Standard Deviation
average distance from the mean
Standard deviation is the same as…
Squared deviation
Degrees of freedom
For samples, instead of (N), use (n-1) in the denominator
What’s the issue with variance of a sample?
the variance of a sample is a little too small for (aka, underestimates) the actual population variance
What is the z score of the top 5% or less
1.65
What’s the z score for being in either the top or bottom 5%
1.96
Standardization
the process of transforming a variable to one with a mean of 0 and a standard deviation of 1.
why do we want to know z scores
we want to know where something where it is located in the distribution of scores.
(I.e., how far away a score is from the mean)
tells you the exact
location of the original X value within a
distribution.
standardized
distributions and z scores
z scores help standardize distribution by allowing comparison of different distribution scores
Binomial Distribution
These distributions tell us the probability for a specific number of “successes” to happen, given a probability of success and number of trials.
binomial distributions tell us the results of only two possible outcomes: success or failure.
An example of this is flipping a coin, which can only result in heads or tails.
% of scores lie between 0 and 1 SDs
above the mean.
34.13%
% of scores are between 1 and 2 SDs
above the mean.
13.59%
% of scores are between 2 and 3 SDs
above the mean.
2.15%
% of scores are more than 3 SDs above the
mean.
0.13%
Alpha level
This is the probability level for significance.
Sampling distribution
shows every possible result a statistic can take in every possible sample from a population and how often each result happens
In a perfect relationship between two variables, r squared would be
Equal to 1.00
