Exam 1 Flashcards
Descriptive Statistics
Organizing and summarizing data using numbers and graphs.
Data that we collect or observe (empirical data).
Examples- frequencies and associated percentages, average rank of outcome, pie charts, bar graphs, or other visual representations of data.
Inferential Statistics
A range of procedures/ statistical tests (t-test, chi-square, multiple regression analysis).
Allows us to generalize from our sample of data to a larger group of subjects.
Examples: population- parameter mean, standard deviation
Examples: sample- statistics (standard deviation)
Discrete variable
Discrete variable is characterized by gaps or interruptions.
Referred to as “qualitative data”
They have values that can only assume whole numbers. They can have only one of a limited set of values.
Example- sex, marital status, blood types
Continuous variable
Has no gaps or interruptions. It may take any value within a reference range.
Referred to as “Quantitative data”
Examples- height, weight, BP, final exam scores
Dependent variable
Y
The outcome of interest, which should change in response to some interventions
For example- Final exam score for educational assessment, blood glucose levels for diabetic tests, bio-availability measurement (Cmax)
Independent variable
The intervention, or what is being manipulated. A variable keeps changing its value. It allows us to control some of the research environment.
Predictor variables
Example- temperature levels for tested animals, experimental vs control drug therapy groups, institutional vs community pharmacy.
What are the 4 types of scales for measurement
Nominal, ordinal, interval, ratio
Nominal scale
Named categories with no implied order among the categories
Attributes are only named, weakest scale
Examples- Sex (male, female), Race, Most percentages, yes/no data
Ordinal Scale
Same as nominal, but includes ordered categories. The difference between these categories cannot be considered equal.
Examples- Letter grades, heath outcome, satisfaction scores, agreement levels, rankings, scales, rates, medical conditions
Interval Scale
Same as ordinal plus equal intervals. Data has equal distances between scores, but the zero point is arbitrary.
Example- BP, Time, temperature, lab values
Ratio Scale
Data has equal intervals between points and a meaningful zero point.
Example- BP, Time, temperature, lab values
Population samples
Represent the best estimate we have of the true parameters of that population.
Random sampling
Equal chance of being included in the sample.
Example- use of random numbers table
Stratified Sampling
Population is divided into subgroups (strata) with similar characteristics, then randomly select samples from each strata.
Example- Age groups (age 0-18, age 19-34. etc.)
Selective Sampling
Not random sampling, convenient sampling
Example- select all patients who visited the psychiatric clinic today
Cluster Sampling
Many individual “primary” units that are clustered together in secondary (units can be sub-sampled)
Example- For Q/C sampling, randomly select 10 bottles (secondary) then select 4 tablets (primary) from the top, middle, and bottom of the bottle.
Systematic Sampling
Systematically select subjects as sample.
Example- Every 9th person will be selected.
What is the difference between cluster and stratified sampling?
Stratified sampling seeks to divide the sample into heterogeneous groups so the variance within the strata is low and between the strata are high.
Cluster sampling seeks to have each cluster reflect the variance in the population. Each cluster is a “mini” population.
Symmetric (bell-shaped) distribution
Mean=median=mode
Positively skewed distribution
Mode
Negatively skewed distribution
Mode>median>mean
Why is degree of freedom used?
To correct for the bias in the results that would occur if just n was used
n-1
Variance
The average variability of scores in the distribution measured in squared units of the original score
What is the population variance?
The average squared deviation of scores about their mean.
Which is the property of normal distribution?
A,) Unimodal with continuous data
B.) Mean, median, mode are all equal
C.) Sum of probability of all possible outcomes is equal to 1.0
D.) All of the above
D
For normal distribution, what happens to the standard deviation as the sample size increases?
It decreases
Does inferential statistics use sample or population?
Sample
What is the difference between sample and population?
Sample- those individuals in the study. A sample deals with statistics
Population- the hypothetical (and usually) infinite number of people to whom you wish to generalize. A population deals with parameter
Standard error of mean (S.E or SEM)
Represents the possible variability of the mean itself.
S.E shows how close the man scores from repeated samples will be to the true population mean
Equal to the population standard deviation divided by the square root of the sample size.
Null hypothesis
The hypothesis to be tested
There is no difference between 2 population means
Hypothesis A
Alternative hypothesis
Set of hypothesis that remain tenable when the null hypothesis is rejected.
Hypothesis A is false
There is a difference between “sample” and “population”
Level of significance testing
Does a particular sample belong to a hypothesized population? Steps: 1.) Null and alternative hypothesis 2.) alpha level (commonly 5% or 0.05) 3.) p value
P value
Probability of observing what you observed base don the study sample data
If the p value is less than the predetermined alpha value, we reject the null hypothesis.
Statistical Power
Power is the ability of a statistical test to show if a significant difference truly exists.
Termed 1-beta (1-b)
Type I error
Rejecting the null hypothesis when it is actually true
alpha level determines the chance for type I error
Example- sending an innocent person to prison
Type II error
Accepting the null hypothesis when it is actually false.
Beta, B is the probability of concluding there was no difference when, in fact, there was one.
Freeing a guilty person
What happens when the null hypothesis is true and you accept it?
Correct
1-alpha
What happens when the null hypothesis is false and you accept it
Type II error
beta
What happens when the null hypothesis is true and you reject it
Type I error
alpha
What happens when the null hypothesis is false and you reject it?
Correct
Power= 1-beta
Standard Scores (Z score)
Z score is number of standard deviation above or below the mean for a particular score
Z tests
Involve a dependent variable. Useful when comparing a sample statistic to a known population parameter (mean and SD).
Accurate only for large samples
Z test steps
1.) Make the null hypothesis
2.) State the alternative hypothesis
3.) State a decision rule
alpha-0.05, 95% confidence interval; critical value=1.96
4.) Compute relevant z statistics
5.) Evaluate the null hypothesis
Confidence Intervals
The result of estimate is a range of possible outcomes defined as boundary values or confidence limits.
95% confidence interval
z=1.96; alpha=0.05
95% chance that the true population mean falls within the range. There is a 5% chance that the truth is outside the range.
68% C.I
z=1
96% C.I
z=2
98% C.I
z=2.58
As sample size increases, what happens to CI?
The width of CI decreases
Two-tailed test
Nondirectional test u1=u2
One-tailed test
Directional u>20
What are t tests used for?
Comparing one sample to a known population parameter
Comparing 2 samples to each other and making inferences to their population
What are t-tables used for?
To adjust the z-values of a normal distribution to account for sample sizes
One-sample t test
Can be used to either estimate the population mean or compare the sample mean to an expected population mean
