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NU 406 Final (Stats)
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Terms in this set (118)
What is ANOVA?
Analysis of Variance
 examines differences between means in 2+ groups
Requirements for ANOVA test
 Outcome variable: interval or ratio
 Independent groups (not r/t each other)
*Preferred* for ANOVA test:
 Random assignment
 Normally distributed within population
 Homogeneity of variance
What test is used to test for homogeneity of variance?
Levene's test
What is the difference between the ANOVA test and the ttest?
ANOVA has more than 2 groups, Ttest is only good for differences in means with 2 groups
(can be done with just 2 and would get same results as ttest, but this test can be used with more than 2 groups)
ANOVA produces an....
F statistic (ratio) and corresponding p value
The F ratio produced by ANOVA test tells the extent to which...
group means (M) differ
The ANOVA test examines differences ___________ the groups and difference __________ the groups
between; within
If the difference *between* groups is not greater than *within* the groups, then...
no significance
How is Fratio found?
Difference between group (MS) / difference within group (MS)
If the F ratio is close to 1, it is (likely/unlikely) to be significant for differences
*but always check your p value to know for sure
unlikely
Degrees of Freedom for ANOVA formula(s)...
Df
between
groups: k (# of groups)  1
Df
within
groups: N  k
ANOVA Df: df between groups + df within groups
The F ratio finds a statistically significant difference between at least...
2 of the group means
 however it does not tell where the difference is, further testing is needed
What kind of tests are used to see where the difference between means of groups is?
Post Hoc tests
 Sheffe, Bonferroni, Tukey's, Fisher's LSD, GamesHowell, and more
Null and Research hypothesis for ANOVA
Null: there is no difference...
H0: M1 = M2 = M3
Alternative: There is a difference ...
H1: M1 ≠ M2 ≠ M3
What is Repeat Measures ANOVA?
Dependent samples: same DV is measured over time in subjects
 Finds change over time iN DV with exposure to the IV
What are some concerns about Repeat measures ANOVA
Carryover effects
Position effects
What are carryover effects?
When the previous treatments continue to have an effect through the next treatment
What is the Position effect?
When the order of treatment impacts the outcome
How can you maybe overcome carryover and position effects?
Carry over effect
 washout effect stop all interventions, let the effect of the first thing wash out before doing next intervention  but this can be bad...
Position effect
 switch order so some ppl get Tx's in one order, others in another order
Mixed Method ANOVA has two groups, looking at....
 Differences between groups (independent) &
 Differences from pretest and posttest for each group (dependent)
MixedMethods ANOVA finds this....
change between groups and over time within groups
*Chapter 11  Correlational Coefficients*

Correlational Coefficient...
a descriptive statistic that indicates the strength of the relationship or association between two variables
What are the requirements for a correlational coefficient?
1 sample; at least 3 subjects (prefer >50)
For a correlational coefficient, at least 3 subjects are required, but how many are preferred?
>50 preferred to address concerns
 normal distribution
 Homoscedasticy
What is homoscedasticity?
homogeneity of variance
What type of correlation coefficient should be used if there is nominal data for at least one variable?
ChiSquare
What type of correlation coefficient should be used if there is ordinal data for lowest lvl of measurement *or* there is interval/ratio data, if not normally distributed
Spearman Rho (p)
What type of correlation coefficient should be used if there are two or more variables that are interval/ratio lvl data and are normally distributed
Pearson's correlation coefficient (r)
ChiSquare has __________ data for at least one variable
nominal
Spearman Rho (p) correlation coefficient is used if...
Ordinal data is lowest lvl of measurement
or
interval/ratio data if normally distributed
Pearson's correlation coefficient (r) should be used if...
There are 2+ variables that are interval/ratio lvl data and are normally distributed
Pearson's correlation test determines the extent of the relationship between these 2+ variables (to what extend is a change in one associated with a change in another)
How is Pearson's correlation coefficient expressed as?
r
*this is also the effect size
Null and Research Hypothesis for correaltional coefficients
H0: There is no relationship between the number of overtime hours worked and the number of medication errors in the nurses at XYZ hospital. H0 r = 0
H1: there is a relationship between the number of overtime hrs worked and number of medication errors in the nurses at XYZ hospital
Formula for degrees of freedom with pearson correlation
based on pairs of values for the two variables being correlated, so...
df = N 2
What is the strength of correlation determined by?
absolute value of r
Strength of correlation:
<0.3 = weak relationship
0.3  0.5 = moderate relationship
>0.5 strong relationship
Effect size
If there is a weaker relationship, then what is needed to be able to find the relationship?
larger sample size
Positive vs Negative association:
 One variable increases and the other decreases = positive association
 One variable increases and the other decreases = negative association
*notes: direction of association is different than strength of correlation
Pairwise / pairwise deletion
Pairwise  noting # of ppl that completed each part
Pairwise deletion = method of handling missing values in which only the cases/respondents with complete responses are considered for each calculation or analysis
How is significance expressed for Correlation?
expressed as an r value with a corresponding p value
 large correlation coefficients may be insignificant if sample is very small
 small correlation coefficients can be significant if sample is very large
Remember to check p value
What are some things to consider when choosing the best correlational coefficient?
 Do you have 1 independent sample?
 Are you looking for a linear relationship between two variables in this sample?
 What is your lvl of measurement?
Choosing the best Correlation Coefficient to use based on lvl of measurement:
 Nominal: Chisquare
 Ordinal: Spearman's
 Interval/ratio: Pearson's (N ≥50 subjects)
What is Percent of Variance?
the difference in 1st variable from 2nd variable
How do you calculate the percent of variance?
r² (coefficient of determination) x 100
 if r=0.78 for study hours and exam grade
 (0.78 x 0.78) = 0.6084
 0.6084 x 100 = 6084% of difference in exam grade is from # of study hours
This r value of percent of variance is clinically important (significant)
r values ≥0.3 (9% variance)
*Chapter 12  Regression Analysis*

Regression is a statistical technique to...
quantify relationships, then predict future events
What are the 3 different types of regression?
 Linear regression
 Multiple regression
 Logistic regression
Linear regression is a technique for identifying/analyzing...
the relationship between 1 interval/ratio IV (x axis) and 1 interval/ratio DV (y axis)
Linear regression
If a linear relationship is found when these interval/ratio IV and DV) are graphed, the slope can tell you:
 How much the predicted value of DV changes
 When there is 1 unit of change in IV
Yi = b0 + b1Xi + Ei
error regression model
What is *residual* in regards to linear regression?
The difference between where the data actually falls and where the linear regression line predicts they will fall
*designated with greek epsilon
*also called prediction error
Residual regression is also called...
Prediction error
A lower residual (prediction error) means...
a better fit of the prediction line and the data
(the prediction line is more accurate in predicting the data)
Residual (prediction error) is looking at a single ____ and single ____
IV, DV
Multiple regression is a statistical method used when..
looking at the relationship between one DV and multiple interval/ratio IVs
Multiple regression formula...
Yi = a + B1X1 + B2X2 + E
A = constant, value when x = 0
B = regression coefficient
E = error term (implies est)/residual
What are B values in multiple regression?
Regressional coefficients
 Show the change in the D.V. for a oneunit increase in the I.V. if the other I.V.s are held constant
What does it mean if the B value (regressional coefficient) in multiple regression is negative?
My notes: When B value is negative, doing nothing in the lvl of this IV decrease the lvl of the DV (outcome)
Shelena's notes: When B value is () inc in the lvl of this IV dec the lvl of the DV (outcome)
Quizlet: decreasing IV increases the DV
Each regression model has a corresponding R², which tells you...
tells how much/the percent of variance in the D.V. (outcome) that is explained by the I.V.s in your regression model
Note: If R² is 0.74, then the variables inlcuded in your regression model explain 74% of variance in outcome

R² always increases with..... even if...
R² always increases with additional I.V.s, even if the added I.V.s are not significant
Adjusted R² explained
Adjusted R² is a more conservative estimate of the R².
 It's a better option when there's a large # of I.V.s (bc it tells you the additional varaince in DV acounted for when you add another IV), especially with small samples

When
sample size is small, researchers sometimes report the adjusted Rsquared to avoid overestimating the amount
of variance in the dependent variable explained by the independent variables in the equation.
What is Standard Error of the estimate?
Tells you the average amount of error in the predicted outcome using this regression model.
 You want to minimize standard error of estimate (want it as close to 0 as possible) to make prediction as accurate as possible
How to determine significance with multiple regression?
Look at pvalue for each IV's R²
 Can have an overall significant R², but have I.V. that is not significant
 Insignif variable doesn't add to the ability to predict the outcome
Logistic regression is a method for analyzing..
the relationship between multiple IVs and a single DV that is binary
 Binary  only two categories i.e. yes/no, alive/dead
 IV can be nominal, ordinal, or interval/ratio
Logistic regression generates an _____ ratio
odds ratio (OR)
Logsitic regresion generates an odds ratio (OR). This helps to...
explain results to the public
How to calculate odds ratio (OR)
probability of the outcome occurring divided by the probability of the outcome not occurring
*Chapter 13*

Epidemiology is...
the study of distribution of disease
What are the 3 types of epidemiology study designs?
 Cohort
 Case Control
 CrossSectional
This type of epidemiology study design begins with exposure and follows for the outcome (prospective)
Cohort
This type of epidemiology study design begins with the outcome and looks back for exposure (retrospective)
Case control
This type of epidemiology study design assess exposure and outcome at the same time
Crosssectional
(book) A cohort study is..
A prospective design that follows a group of individuals over time to see who develops the outcome of
interest.
Incidence is...
the number of new cases in a particular timeframe
How to calculate incidence rate:
number of new cases/population at risk x100
What is the only type of study design that gives incidence data?
cohort
Incidence can be used to calculate...
Relative risk
(also known as Risk Ratio (RR))
Formula for Relative Risk
Incidence rate of exposed group/incidence rate of unexposed group
Relative Risk (RR) = A/(A+B)/C/(C+D)
A =
B =
C =
D =
A = subjects with exposure and disease
B = subjects with exposure but without disease
C = subjects without exposure but with disease
D = subjects without exposure and without disease
Those diagnosed with the disease during the study (cohort) are _______ cases  cells ___ and ____
incidence; A and C
Relative Risk means this..
Exposed group was (number of RR) times as likely to get sick as the unexposed group
If the Relative Risk (RR) is significant, this means...
 Exposure occurred before the disease
 Exposure is considered a risk factor for this disease
 Incidence data helps establish causality
Relative Risk (RR) interpretation:
If RR <1, this means..
the exposed group had fewer cases/less incidence  possible protective effect
Relative Risk (RR) interpretation:
If RR = 1, this means...
No association between exposure and illness
Relative Risk (RR) interpretation:
If RR >1, this means...
Exposed group has higher incidence/more cases  possible risk factor
Confidence intervals instead of p are a range of values that...
range of values that estimate where parameters fall
 useful for reporting results accurately
"I am 95% confident that the mean score for the population will fall between ______ and _______."
Confidence intervals are useful for...
reporting results accurately
Confidence Intervals: 0.871.5
Is this significant? Why/why not?
Not significant because 1 is in middle  one value is below 1 (protective effect), and other is above 1 (risk)
Confidence Intervals: 12.214.1
Is this significant? Why/why not?
Significant
 both are on the same side of 1
Confidence Intervals: 0.750.92
Is this significant? Why/why not?
Significant
 both are on the same side of 1
Confidence Intervals/Ratios are usually at...
95% confidence (a = 0.5)
 Researcher is 95% confident that ACTUAL value in population is between these two numbers
If the Confidence Interval range includes 1, then..
it is not significant
Cohort studies frequently use attack rate to...
determine the likely source of an epidemic or outbreak
Formula for Attack Rate:
Incidence in exposed group (those who got sick)/all exposed to particular agent x100

You calculate the attack rate by taking all those exposed to the agent of interest and putting that
number in the denominator. You then consider, of this group, who got sick and put that number in the
numerator. Finally, to make it a percentage you multiply by 100.
What is a case control study again?
A study design that starts with the outcome of interest and looks back to determine exposure (retrospective)
 compares ppl with and without disease to find common exposure
Case control studies compare people with and without disease to find...
common exposure
With Case Control studies, there is no _________ data or ________ _______.
incidence data; relative risk
WIth Case Control studies, there is no incidence data or relative risk. Instead, case control studies use _________ _______.
prevalence cases
Case Control studies use prevalence cases.
Use an approximation of RR > Odds Ratio (OR).
Odds Ratio is..
the estimate of being sick
Formula for Odds Ratio (OR):
Odds that a case was exposed/odds that a control was exposed
A/C / B/D or AD/BC
In logistic regression, beta values can be converted to...
odds ratio
_______ ________ in logistic regression can be converted to odds ratio
beta values
What does Odds Ratio mean..?
Odds of a sick person being exposed is (OR number) times likely
What does an Odds Ratio (OR) of 30 mean..?
 If p value is significant, odds of a sick person having been exposed is 30x more than that of a well person
OR approximates the RR  it estimates that if exposed, approximately 30x more likely
Crosssectional collects data about...
about presumed cause and presumed effect at the same time
Because CrossSectional studies collect data abt presumed cause and effect at the same time, they cannot/are weak at...
cannot establish which comes first; weak at proving causation
Crosssectional studies
What is attributable risk?
The amount of disease (outcome) in exposed group due to a particular exposure
Formula for attributable risk:
Incidence rate in exposed group  incidence of unexposed
What is proportion of excess risk and how do you calculate it?
Attributable risk (AR) / incidence exposed
Other advanced statistics tests

The Analysis of covariance (ANCOVA) test is used to...
statistically control specific extraneous variables that may influence the dependent variable
Canonical correlation test examines...
≥2 IVs and ≥2 DVs
The Multivariate analysis of variance (MANOVA) test evaluates...
evaluates differences between ≥2 groups on ≥2 DVs
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