What are statistics
o A branch of mathematics used to summarize, analyze, and interpret a group of numbers or observations
o Read and understand research reports, produce your own research, and increase your reasoning skills
Role of statistics in the research process
o To organize and summarize your data so that you can read and understand the reports, come to conclusions, produce research.
Descriptive vs. Inferential statistics
o Descriptive: Procedures used to summarize, organize, and make sense of a set of scores or observations
� Typically presented in a graph, table, or as a summary stats ("on average...")
o Inferential: use descriptive stats to make a prediction about unkno
Discrete vs. Continuous variables
o Continuous: measured along a continuum at any placed beyond the decimal point
o Discrete: measured in whole units or categories that are not distributed along a continuum
� Score can not fall in the middle of a whole number units
Quantitative vs. Qualitative variables
o Quantitative: can be continuous or discrete; will be numeric
o Qualitative: varies by class, often represented as a label and descries nonnumeric aspects of phenomena
� Vary by class, non numeric
Population vs. sample (& symbols associated with each)
o Population: the set of ALL individuals, items, or data of interest ("N")
o Sample: a set of selected individuals, items, or data taken from a population of interest ("n")
Parameter vs. Statistic
o Population parameter: a characteristic (usually numeric) that describes a population
o Sample stat: a characteristic (usually numeric) that describes a sample
�results of data, not number of those people or things looked at
Properties of Scales of Measurements
o Order: does a larger number indicate a greater value than a smaller number?
� Order of numbering important?
o Differences: does subtracting two numbers represent some meaningful value?
o Ratio: does dividing (or taking the ratio of) two numbers represen
Differences between scales of measurement (nominal, ordinal, interval, ratio)
o Nominal: value assigned to categories, can not be ranked, number assignment has no meaning (zip code)
� Order, differences, and ratio DOES NOT MATTER
o Ordinal: assign numbers to categories that corresponds to ranks, responses can be ranked from high to
Frequency Distribution Tables (grouped and ungrouped)
Grouped: intervals (13-16, 17-20)
� Rules (grouped): each interval is defined (can't be 17 and below)
� Each interval is the same between each interval
� No intervals overlap (list ALL intervals, even if frequency of 0)
� All values are rounded to the sam
How to find and complete different types of frequency information (e.g., f(X), two methods for finding sums of scores)
o f(x): frequency of scores- how often are we getting values falling in this interval
Graphs (bar graph, histogram, frequency polygon, pictogram, etc.)
o Histograms: (line graph), continuous data
� Rules: vertical rectangle represents each interval, and the height equals the frequency recorded for that interval
� The base of each rectangle begins and ends at the upper and lower boundaries of each interva
How to create a graph, types of graphs, when they are used, characteristics of each
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Measures of central tendency (mean, median, and mode)
o Mean
� Population Mean ?=?X/N
� Sample Mean M=?X/N
� The mean is the balance point in a distribution
o Median
� Middle value in a distribution of data listed in numeric order
� (n+1)/2
o Mode
� Value in a data set that occurs most often
� To find it lis
What central tendency is and what it is for
o Stat measure for locating a single score that is most representative or descriptive of all scores in a distribution (tend to fall in the center of the distribution) Measures of central tendency are stated differently for populations and samples but are
Know the three types, when it is best to use each type
o Mean: when data is normally distributed (symmetrical), when data is measured on an interval or ratio scale
o Median: when the data is skewed distribution, when the data is measured on an ordinal scale
� Outlier: extreme score that is pulling the distrib
Weighted mean
o Combined mean of two or more groups of scores, where the number of scores in each group is disproportionate or unequal
� More weighted on the groups with a larger sample size
Mw=?(Mxn)/?n
Characteristics of the mean
o Changing an existing score will change the mean
o When you increase the value of an existing score, the mean will increase
o When you decrease the value of an existing score, the mean will also decrease.
o Adding/Removing
� Adding a new score or complet
What variability measures
o A measure of the dispersion or spread of scores in a distribution that ranges from 0 to positive infinity
o Low: more alike, bunched up
o High: different, spread out
o WILL NEVER BE A NEGATIVE SCORE
Measures of variability (range, standard deviation, variance)
o Range: the difference between the largest value (L) and the smallest value (S) in a data set
o Variance: a measure of variability for the average squared distance that scores deviate from their mean
o Standard deviation: measure of variability fro the a
How to calculate each measure of variability (for variance standard deviation, know how to calculate for both sample and population; for variance, know how to use the deviation method and the computational method)
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Deviation scores
o The difference of each score from its mean
Sum of squares
o The sum of the squared deviations of scores from their mean
Understand the theory behind the formulas for sample and population variance
o Population: the average squared distance that scores in a population deviate from the mean
� SS/N
o Sample: average squared distance that scores in a sample deviate from the mean
� SS/(n-1)
Characteristics of standard deviation
o Measure of variability fro the average distance that scores deviate from their mean (estimate for the average distance scores deviate from the mean)
� 99.7% of data fall within 3 SDs of the mean
� It is always positive
� It is used to describe quantitat
X
a score, individual score
f(x)
frequency of score
E
sum of
N
population size
n
sample size
u
mu, population mean
M
sample mean
To study NCAA athletes at a local college, a researcher measures behavior in a portion of all athletes at the college. What type of statistics can the researcher use to draw conclusions about the behavior of all athletes at the college?
inferential
A researcher selects a _____ and uses inferential statistics to draw conclusions about the larger _____ .
sample; population
A health psychologist studies food intake by recording two measures: the type of food consumed (high fat, low fat) and the number of calories consumed. Which is a nominal scale measure?
the type of food consumed
State the scales of measurement from least to most informative:
nominal, interval, ordinal, ratio
A researcher places a participant in a room filled with 10 strangers. To measure social behavior, he records the number of different people the participant talks to and the time (in seconds) spent talking. The number of people the participant talks to is
quantitative; quantitative
Qualitative variables tend to be on which scale of measurement?
nominal
A researcher places a participant in a room filled with 10 strangers. To measure social behavior, he records the number of different people the participant talks to, and the time (in seconds) spent talking. The number of people the participant talks to is
discrete; continuous
A researcher records the family relationship (brother, son, father, cousin, etc.) of the people who stay in regular contact with loved ones in a nursing hoe. What type of measure is family relationship?
qualitative; discrete
When we say that the actual average height of all adult females in the U.S. is known to be 5'6", we are using:
descriptive statistics
The measured heights of a group of basketball players form:
ratio scale
A researcher measures the following scores: 0, 2, 2, 2, 2, 2, 4, 4, 4, 4, 0, 0 , 0, 0, 0, 0, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 0, 2, 4, 2, 4, 4, 4, and 0. Should these data be grouped?
No, because the number of different scores is small
The influence of one or more extreme scores in one direction is most pronounced on the value of the:
mean
A researcher constructs the following simple frequency distribution. How many scores were measured in this study?
Scores Frequency
12-14 8
9-11 12
6-8 4
3-5 6
0-2 10
40 scores
Each of the following is a rule for constructing a histogram, except:
frequencies are plotted at the midpoint of each interval and the line connects each plot
A bar chart is similar to a histogram, except that in a bar chart, each rectangle ___ the adjacent rectangles at the boundaries of each interval:
does not touch
The mean is the balance point of a distribution, which means that it is:
not always located at the center of a distribution of scores
The median is:
a. the preferred measures of central tendency when outliers are in the data set
b. the middle value in a distribution listed in numerical order
c. at the 50th percentile of a cumulative percent distribution
The mean for a distribution of scores is M = 3.2. If we remove an existing score equal to 3.2, then what will happen to the mean?
the mean will remain the same
The mode is the primary measure of central tendency to describe data on which scale of measurement?
nominal
A researcher measures a data set with a range equal to 12. Which of the following data sets has a range equal to 12?
0, 9, 3, 12, 10, 7
Which of the following describes the calculation for the sum of squares (SS) using the deviation method?
the sum of the squared deviations of scores from the mean
How is the formula for the sample variance different from the formula for the population variance?
SS is divided by the degrees of freedom for sample variance in the denominator of the formula for sample variance
The sum of the deviation of scores from their mean is zero. To avoid this result, each deviation is
squared
The sample variance is an unbiased estimator of the population variance when we:
divide SS by (n - 1) & divide SS by df
The _____ is the square root of the _____
standard deviation; variance
The standard deviation is most informative for describing what type of distribution?
normal distribution
Suppose that at least 68% of scores in a normal distribution fall between a score of 7 to 10. Using the empirical rule, what is the approximate mean and standard deviation of these data?
mean = 8.5, standard deviation = 1.5
Suppose a normal distribution has a mean of 8 and a standard deviation of 2. What is the range of scores within which at least 95% of scores are contained?
4 to 12
The standard deviation is almost always reported with which measure of central tendency?
the mean