Analyzing Data: Understanding Statistics
what is a t-test?
Often used to test null hypothesis regarding observed difference between two means
the shape of distribution if the data in a frequency distribution are used to construct a figure called
frequency polygon
how is range of a set of scores calculated
highest score minus lowest score
Is the "range" or the "interquartile range" a more reliable statistic?
interquartile
what is another name for margin or error
confidence interval
sample size (t-test)
larger samples are less likely to have an observed difference based on sampling errors
t values rely on
degrees of freedom, which help to distinguish significance based on different amounts of data
which variable type corresponds to the outcome being measured
dependent variable
one way to describe a quantitative data is to prepare a
frequency distribution
what does r -1.00 indicate
perfect negative correlation. As one value goes up the other value goes down in a perfect line
Does a distribution with a tail to the right have a "positive" or a "negative" skew?
positive
in most population income has what type of skew
positive
a measure of how likely something is. In statistics, it considers how likely a random sample is to represent the true values if you asked the entire population.
probability
why is it important to know the scale of measurement when using statistical test
they largely determine the appropriate statistical test to carry out
Bivariate
two variables
Standard deviation measure
variability
dichotomous
variable is a categorical variable for which there are only 2 choices
a researcher ask is voting behavior differs based on one's race. Which of these variables is dependent?
voting behavior
The amount of variation in the population (t-test)
when a population is very homogeneous (similar), there is less potential for sampling error, so less variation leads to a lower p-value.
size of difference between means (t-test)
when the means being compared are more different, they are less likely to be explained by sampling error/lower value of p.
What is regression
widely used approach to statistical data analysis and looks at the linear association between two variables
what does r 1.00 indicate
a perfect positive correlation. As one value goes up the other value goes up in a perfect line
Do researchers reject the null hypothesis when the probability of its truth is high or when the probability is low?
low
Mathematical techniques used to analyze data that is numerical or that has been converted into number form AND based on the use of a sample drawn from the population (estimate value; m)
statistics
The null hypothesis says that true difference equals what numerical value?
0
Significance tests are designed to determine the probabilities regarding the truth of what hypothesis?
null hypothesis
N refers to
number of cases
Frequencies
number of times an answer was given by respondents.
when researchers study a sample are the results called the true results or the observed results
observed results
Chi-square test significant values vary and are based on
on degrees of freedom and significance in relation to the test's p-value (typically .05).
Univariate
one variable
if al individual in a group have the same score what is the value of the standard deviation for the score
0
what is the base for proportions
1
The Chi-square test ask?
"how likely is it that an observed distribution is due to chance (null hypothesis)?
percentage for different groups are exposed on a common scale with what base
100
α ≤ .05 (5%) means confidence level
95%
how is the mean calculated
Add up the scores and then divide by the number of scores
ordinal definition
Answers have a rank order with no specified distance between each category
"Pearson r" stands for what words?
Pearson product-moment correlation coefficient
What is confidence level
Percentage of all possible samples that could include the true population parameter within a suggested range
The expression p<.05 stands for what words?
The probability that the null hypothesis is correct is less than 5 in 100.
Type II Error
When the researcher fails to reject the null hypothesis but it should have been rejected.
when the relationship between two variables is perfect and inverse, what is the value of r?
-1.00
what causes t-test to yield low probability?
-sample size -size of difference b/w means -amount of variation in the population
If 600 individuals in a population of 1,000 are Democrats, what is the corresponding percentage of Democrats?
60%
in a normal distribution, what percentage lies within one standard deviation unit of the mean
68%
α ≤ .01 (1%) means confidence level is
99%
what does regression tries to answer?
How much variation in the dependent variable can be explained by variation in the independent variable(s)?"
what branch of statistics helps researchers to estimate the effects of sampling errors on their results
Inferential
what is Person correlation coefficient
Measures degree of linear correlation between two variables
what is Chi-square test
Tests for differences between frequencies of values that are observed versus those that were expected.
what is the formal definition of the mean
The value around which the deviations sum to zero
Type I error
When the researcher rejects the null and concludes that a study supports the research hypothesis when the null is in fact correct.
what is the term for the cutoff value that is commonly used in statistics to set limit for accepting that the results from a statistical test are due to change?
alpha < or = to 0.5
ANOVA stands for
analysis of variance (F)
do researchers use univariate or bivariate analyses to examine the relationship between 2 nominal variables
bivariate
what value is 100 minus the alpha
confidence level
Two-way ANOVA
considers whether differences when researchers use a two-way classification
which brand of statistics helps researchers to summarize data so they can be easily comprehended and is a frequency distribution?
descriptive
is a relationship direct or inverse when those with high scores on one variable have high scores on the other AND those with low scores on one variable have low scores on the other?
direct
What is the interquartile range?
divides a sample of any size into quarters, then cuts off the top and bottom quarter, looking at only the middle 50%
statistics use a sample to make __ about a population
inferences
Are significance tests associated with "descriptive" or "inferential" statistics?
inferential
Which two scales of measurement have equal distances among the scores they yield?
intervals and ratio
Which average is defined as the balance point in a distribution?
mean
which average is usually reported when the standard deviation is reported?
mean
what is null
means zero, empty, or nothing
what is the synonym for the term average
measure of central tendency
Should the "mean" or the "median" be used with ordinal data?
median
which one of the three averages is very seldom used in formal reports of research AND is defined as the most frequently occurring score?
mode
when researchers use a large sample, are they more likely or less likely to reject the null hypothesis than when a researcher uses a small sample?
more likely
ANOVA can compare
more than 2 means
if a descriptive statistics involves more than 2 variables what is it called
multivariate
if a distribution has some extreme scores on the right but not on the left it is said to have what type of skew
negative
if a distribution is skewed to the left, does it have a positive or negative skew
negative
what does the null hypothesis say about difference between two sample means
no true differences b/w the means b/c the values are the results of the chance errors created by random sampling or sampling errors
if researcher asks participants to name country in which they were born, the researcher is using which type of scale measurement
nominal
what is the name of the curve that is symmetrical
normal curve
the "bell curve" is a nickname for what
normal distribution
When data from the entire population are analyzed, the resulting values are called (actual value; M)
parameter
what is the name of the statistic that describes how many participants per 100 have certain characteristics AND proportion of respondents that gave each type of response?
percentage
a researcher asks if voting behavior differs based on one's race. Which of these variables is independent?
race
Does the term sampling error refer to "random errors" or to "bias?"
random errors
what statistics discussed are measures of variability
range and interquartile range
Mean
same as average: summarizing a single variable by adding all values and dividing by the number of values
the observed difference (null hypothesis) was created by
sampling error
What is an alternative way of saying a researcher has rejected the null hypothesis?
statistically significant
By studying samples, do researchers obtain "statistics" or "parameters"?
statistics
One-way ANOVA
tests the influence of only one independent variable (IV) on the dependent variable (DV).
a null hypothesis suggest that
that the result of study or experiment shows that results were not significant.
what is meant by term variability
the amount by which participants vary or differ from each other
Median
the middle value when all values are ordered from smallest to largest
what is one incorrect way of saying a researcher has failed to reject the null hypothesis.
the researcher should not say they accept the null hypothesis
If an ANOVA yields p<.05, should the null hypothesis be rejected?
yes 0.5 or less
nominal definition
•Answers are names not numbers with no meaningful rank order
ratio definition
•Answers have a rank order with a specific distance and a zero that equals "none" of the characteristic
Interval definition
•Answers have a rank order with a specific distance but no zero that equals "none" of the characteristic
what is ANOVA
•Compares the means of two groups to see if they truly reflect a difference.
What is descriptive statistics?
•Describes or summarizes data •May describe one variable or the relationship between two or more variables
What is inferential statistics?
•Infers or estimates how well sample data represent the population •Used to generalize results to the population •Presents the statistic as well as its likelihood of being an accurate estimate
