First exam based on chapters 1-5 Flashcards
Two meanings of statistics
formal & informal
Formal Statistics
a branch of math that focuses on organizing, summarizing, analyzing and interpreting data in a table or graph or numerically
Informal Statistics
numbers representing something
What do we use to analyze and interpret data?
Inferential stats
inference stats
make a inference or draw a conclusion from a sample from a population
Data
the info we gather from people, places and things
two types of formal stats
descriptive & inferential
descriptive stats
organize & summarize data
inferential stats
analyze & interpret data
variable
a characteristic that can assume different variables ex:height
value
a possible number or category a score can assume, these belong to a variable
score
the value of a variable for a specific person, place or thing
two types of variables
numeric & nominal
numeric variables (quantitative variable)
variables whose values are numbers, includes ordinal & interval
(equal) interval variables
the distance and difference between two sequential values is the same
ordinal variable
categorical variable includes categories divided into groups and are relatively ranked, ex: class rank
ratio variable
has an absolute zero
What is the one benefit of frequency tables?
they provide an organized overview of how often values occur in a group of scores
How do you calculate the percentage on a frequency table?
You divide the frequency by the total number of scores, N=30 and the frequency is 1 the perfect is 3.3%
where do the values and frequencies go on the frequency graph ?
the values go on the x-axis & the frequencies go on the y-axis
Frequency distributions
the shape of a frequency graph reflects the distribution of scores across values of a variable, characterize the pattern of data
unimodal
one highest point in the graph, this is the most frequent
(ex: scores on an IQ test)
bimodal
two equally high points on a distribution (ex: age of people at a park)
rectangular distribution
all values of the same frequency (ex: number of children in each grade)
roughly symmetrical
one side of the face is the same as the other, a mirror image of the other
positively skewed
skewed to the left side
negatively skewed
skewed on the right side
mean
average of the scores, add up all the scores and divide them by N
Σ
sigma
N
number of scores in our group of scores
With means, averages should never be applied to ?
individuals, they are only calculated from individuals
mode
most common value, it is the central tendency for nominal variables
median
middle score, when arranged from lowest to highest
variance table
4 columns, X, M, X-M, X-M^2
X
score to the people in particular the raw score
variance steps
- subtract the mean from each score
- square each of these deviation scores
- sum the squared deviation scores
- divide the sum of squared deviations by N
standard deviation steps
- calculate the variance (SD^2)
- take the square root of the variance
X is a
raw score
Z is a
standardized score that talks in Standard deviation units, they are comparable and combinable
Z score formula
Z=X-M/SD
X-M is a deviation score what does that tell us?
It tells us how far away the X is away from the mean (M)
What is the goal of the z-score?
to convert the raw score to standard deviation units
What happens if the z-score is negative or positive?
Positive- the raw score is above the mean
Negative-the raw score is below the mean
How are sample stats represented?
with roman letters like M, SD, SD2
Sample statistics can change from sample to sample because they are subsets of the population, each sample would be different
How are population parameters represented?
Greek letters
mu (μ) -mean
σ-standard deviation these are fixed quantities
conceptual interpretation
tells us the number of standard deviation units the raw score is above or below the mean
How do you calculate a z score back to a raw score?
X= ZxSD + M
substantive interpretation
applies it’s meaning to the specific scenario
NHST (Null hypothesis significance testing) Step 1
Restate your research question into hypotheses about population,
Null hypothesis H(0)
Research hypothesis H(1)
Null hypothesis
population 1 = population 2
meaning there is no difference
Research hypothesis
population 1 mean is greater than (>) population 2 mean
Population 2 in research hypotheses is?
people in general
Step 2 of NHST
determine characteristics of the comparison distribution under the null hypothesis
What do we do if our sample z-score exceeds the critical cutoff z-scores
we reject the null hypothesis
