# Statistics by Sarah

## Terms

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Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities. Sta
Statistics
Descriptive statistics are used to describe the basic characteristics of the data in a study. They provide simple summaries about the sample being measured. They can be expressed in numerical and/or graphical form. They form the basis of virtually ever
descriptive stats
Inferential statistics are used to draw conclusions about a population based on information contained in a sample. Information is obtained from a sample and generalized to a population.
inferential stats
A value, or quantity, that represents a characteristic of a population such as the population mean or standard deviation.
parameter
The various values that a variable may assume. For example, red, white, and blue are among the levels of the variable â€œcolor.â€ Levels of the variable â€œG.P.A.â€ include: 2.5, 3.2, and 4.0.
levels of variable
A variable whose levels are described numerically. Examples include temperature, % body fat, and time.
Quantittive
A variable whose levels are described with words or phrases. Examples include color (red, white, blue), gender (female, male), and size (small, medium, large).
qualitiative
A quantitative variable with an infinite number of possible levels, limited only by the measuring instrument. Examples include height, weight, and distance.
continuous
A variable, either qualitative or quantitative, with a finite number of levels that cannot be subdivided meaningfully. Examples include heart rate, IQ, and color.
descrete
Variables are categorical, qualitative, and discrete in nature. Although numbers can be used to represent levels of the variables, the numbers are treated as labels. Examples include brand of shoes, Social Security number, and gender.
nominal
Variables are categorical and discrete in nature. Unlike variables at the nominal level, variable levels at the ordinal level of measurement can be rank-ordered meaningfully. Examples include finish position in a race (1st, 2nd, 3rd, . . .) and t-shirt
ordinal
Variables at this level may be quantitative or qualitative, discrete or continuous. They possess the characteristics of ordinal level variables with the added characteristic of equal intervals between levels. Examples include temperature (F), shoe size,
INTERVAL
Ratio level variables possess all of the characteristics of interval level variables with the added characteristic of a measurement baseline. This baseline represents a zero point on the measurement scale or an absolute absence in quantity of the variabl
ratio
An unscientific method of problem solving in which people cling to certain beliefs regardless of the lack of supporting evidence.
tenacity
Data is examined from selected cases and controls to determine differences, if any, in the exposure to a suspected factor. Subjects are not â€œtreated,â€ variables are not controlled, and cause & effect may not be inferred. Example: Incidences of prema
retrospective
A group of healthy subjects is enrolled and followed over time to determine the frequency with which a specific outcome develops. The sample may be grouped according to the presence or absence of a stimulus variable such as smoking history. Example: A g
prospective
A carefully designed study that seeks to determine, under controlled conditions, the effectiveness of a treatment method.
experiment
The degree to which the experimental results can be generalized to the target population. The highest degree of external validity exists when all responses from subjects in the sample can be seen in the population. For example, an average loss of 10 pou
external validity
The degree to which changing the level of the independent variable causes a change in the dependent variable. In an experiment, the highest degree of internal validity exists when all fluctuations in the dependent variable can be attributed to the effect
internal valifity
The Avis effect occurs when subjects in a control group discover they are in a control group and they react by â€œtrying harder.â€ This is a threat to the internal validity of a study.
avis effect
The measurable, observable, or felt improvement in health or behavior not attributable to a medication or treatment that has been administered.
placebo
The Hawthorne effect occurs when subjects in a treatment group improve their performance because they are aware they are being treated or tested. This is a threat to the internal validity of a study.
hawthorne
The Rosenthal effect occurs when a researcher inadvertently influences subjectsâ€™ performances, which consequently affects the outcome of a study. This is a threat to the internal validity of a study.
rosenthal effect
The statistical hypothesis of no difference between means or no relationship between variables. It is the hypothesis that is tested.
null hypoth
An hypothesis that assumes the result (the outcome of the dependent measure) will be in a specific â€œdirection.â€ For example, average BMI will decrease as a result of a training program.
1 tailed test
An hypothesis that does not assume the result (the outcome of the dependent measure) will be in a specific â€œdirection. â€œFor example, average GRE scores will change because of computerized testing.
2 tailed testing
The probability of making a Type 1 error. The researcher sets this probability level as a criterion below which the null hypothesis will be rejected. It is typically set at = 0.05.
alpha level
Rejecting a true null hypothesis. A Type 1 error occurs when the null hypothesis is rejected, indicating a significant difference or relationship, and the difference or relationship does not actually exist in the population. The probability of a Type 1
type 1 error
Accepting, or failing to reject, a false null hypothesis. A Type 2 error occurs when the null hypothesis is retained (not rejected), indicating no difference or relationship, and the difference or relationship does actually exist in the population. The
type 2 error
A measure of variability around the mean. The standard deviation is in the same units of measurement as the mean. For example, if the mean represents average time in seconds, the standard deviation represents variability in seconds.
SD
A distribution made up of all possible mean values from samples of a given size. Sampling distributions are used to create the tables of critical values we use when determining statistical significance.
sampling distribution
The standard deviation of a sampling distribution. A measure of error variability used as the denominator in t statistics.
standard error
Skewness is a characteristic of an asymmetrical distribution. A distribution is â€œnegativelyâ€ skewed when a higher frequency of scores are found above the mean than below it. A distribution is â€œpositivelyâ€ skewed when a higher frequency of scores
skewness
The relative flatness or â€œpeakednessâ€ of a distribution. A relatively flat distribution is called â€œplatykurticâ€ while a relatively peaked distribution is called â€œleptokurtic.â€
kurtosis
An independent variable that has different subjects measured at each level of the variable. (Analyze with an independent t-test or ANOVA).
btw subkects var
An independent variable that has the same subjects measured at each level of the variable. (Analyze with a dependent t-test or repeated measures ANOVA).
within subjects var
A non-parametric test used to compare an â€œobservedâ€ distribution of scores to an â€œexpectedâ€ distribution of scores. This test may be used with nominal and ordinal-level variables.
ch square of goodness fit test
A non-parametric test used to determine if a relationship exists between two nominal or ordinal-level variables.
chi indeependent test
A statistical technique used to determine the linear relationship between two continuous variables. The value of the correlation coefficient (r) ranges from â€“1 to +1.
coreelation pearsons
A statistical technique that allows us to predict a value for a continuous dependent variable from the value of a continuous independent variable. Accuracy of this technique increases as the value of the correlation coefficient increases.
simple linear regression
The degree to which the independent or â€˜Xâ€™ variable explains the variability in the dependent or â€˜Yâ€™ variable. The maximum value of R2 is 1.0 which indicates a perfect relationship between the independent and dependent variables (r will also equa
r^2
A parametric statistical test used to test for a difference between a value, usually a population mean (μ), and the mean of a single sample.
one sample t test
A parametric statistical test used to test for a significant difference between two levels of a between-subjects independent variable.
independent t test
A parametric statistical test used to test for a significant difference between two levels of a within-subjects independent variable.
dependent t test paired
A parametric statistical test used to test for a significant difference between three or more levels of a between-subjects independent variable.
ANOVA
In ANOVA, the degree to which the independent variable explains the variability in the dependent variable. The maximum value of Eta2 is 1.0 which indicates a perfect relationship between the independent and dependent variables (SSE will equal 0 in this s
ETa^2
A multiple comparisons â€œfollow-upâ€ test that allows us to determine the nature of the difference (which means are significantly different) in a significant ANOVA test.
tukeys test

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