Statistics 345 Exam 2

coefficient of determination

represents the actual percentage of variation in one variable that can be accounted for by the other variable.

Sample Size Estimation

required elements -->for Differential stats: expected difference between means, expected SD, DESIRED POWER, and level of significance. -->for correlation: expected r, DESIRED POWER, and level of significance.

Power Estimation

required elements -->for differential stats: expected difference between means, expected SD, EXPECTED N, and level of significance. -->for Correlation: expected r. EXPECTED N, and level of significance

regression analysis

similar to correlation but contains a predictive equation that can be used to predict the value of one variable based on the value of another.

regression coefficient

similar to the correlation coefficient. a measures strength of the relationship between 2 variables during the regression analysis.

Dependent variable

the variable being measured or observed in a study and determines the outcome of the study

significance level

the probability that a mean value will fall in the critical region (making you reject the Ho) when the Ho is actual true and you should have accept it.

Z-score

z = x - mean / standard deviation -->if z-score is > 1.645; Reject Ho -->if z-score is < 1.645; Accept Ho -->contigency tables 2x2.

Friedman Repeated Measured ANOVA

for a rank order variable at the ordinal measurement level (or if interval/ratio variables are not normally distributed) nonparametric.

Repeated Measures ANOVA

determines differences between 3 or more conditions for one group.

Kruskal-Wallis ANOVA (one way)

determines differences between 3 or more groups. -->ex) Question - Are there differences in age between healthy controls, type I diabetics and type II diabetics?

correlation analysis

determines when one variable is significantly related to another variable. ALWAYS COMPARES 2 VARIABLES !!

relationship between power and sample size (n):

-->there is a positive relationship -->as n increases, power also increases.

Reject ho/accept Ho

-if means are different we reject the Ho and accept HA -if means are not different we accept the HO and reject HA.

Critical value and t-value vs. alpha and p-values

-if t value is less then the critical value, then P<0.05 and you reject Ho. meaning you accept Ha, there is . significant difference between conditions/groups -if t value is greater than the critical value, then P>0.05, you accept the Ho. meaning you reject the Ha, there is no significant difference between conditions/groups.

Determining the Critical region

-use a standardized distribution to determine the critical region for a variable -by converting the means for the groups being compared, you can determine if the means are different.

5 uses of Chi-squared distribution

1) not a symmetric distribution, it is skewed right (positively skewed) 2) becomes more symmetric as n increases 3) degrees of freedom (df) = n-1 4) values of X^2 can be 0 or positive (never negative) 5) used to determine significance in Chi-square analysis which compares proportions in a contingency table (2x2 and larger) -->Ho: male blonde = female blonde. male brunette = female brunette -->Ha: opposite of Ho.

Steps for hypothesis testing

1. determine your alternative hypothesis (HA) 2. state your HA as a null hypothesis (Ho) 3. perform statistical analysis to determine if you: -->reject ho and accept HA -->accept ho and reject HA.

McNemar test

A nonparametric statistic used to analyze nominal data from a study using two dependent (matched or repeated measures) groups

Wilcoxon Signed Rank Test

A nonparametric statistical test used to compare two paired (dependent) samples where the outcome of interest is ordinal or continuous with a skewed distribution.

Type 2 error

Accepting the Ho when it is false. -->saying there is no difference when there is a difference. -->similar to false negative test

Mann-Whitney rank sum test

Difference between two groups -->nonparametric -->ex) Question - Are there differences in age between men and women?

One tailed tests

Ha states that the group mean will be either greater or less than the other.

Two-tailed tests

Ha states that there is a difference between means (unequal) w/o further specification.

Type 1 Error

Rejecting a Ho when it is true -->saying there is a difference when there isn't one. -->similar to false positive test

Chi-square analysis

assesses how closely the observed frequencies fit the pattern of expected frequencies it is referred to as a "goodness-of-fit" test -->contigency table of greater 2x2.

Spearman rank-order correlation

a correlation coefficient calculated on variables that are measured on an ordinal scale. NONPARAMETRIC.

independent variable

a factor thought to influence the dependent variable. is often manipulated by the investigator. `

Scatter Plot

a graph that represents the relationship between 2 variables.

Hypothesis

a statement about a population parameter or sample variable that you expect to be true based on available evidence.

Alternative Hypothesis (H1 or HA)

a statement that disagrees with the null hypothesis and states what you expect to be true -->states that the hypothesized group either is not equal to, <, or > population group.

Null Hypothesis (Ho)

a statement that there is no difference between your hypothesized group mean value and the population, control, or placebo value. -->usually expressed as both means being equal.

Analysis of Variance (ANOVA)

a statistical technique that determines whether three or more means are statistically different from one another.

critical value

a value that separates the critical region from accept region

Statistical Power

ability of a statistical procedure to detect a true difference or relationship. "strength of the statistical procedure" -->range of power is 0 to 1 -->usually statisticians want power to be 0.8 or higher.

Sensitivity

ability to identify patients who actually have a condition. -->test has high sensitivity if it has low false negative rate.

specificity

ability to identify patients who do not have a condition. -->test has high specificity if it has low false positive rate

accept region

all the possible mean values that would cause you to accept the Ho

critical(reject)region

all the possible mean values that would cause you to reject the Ho

hypothesis testing

involves comparing a mean value from a specific group or condition to the mean value of population or condition.

Two-way ANOVA

is used when there are 2 combinations of groups to be considered in a data set -->the difference between combinations of groups are called FACTORS.

Pearson correlation

measures the degree and the direction of the linear relationship between two variables. -->numeric value (interval or ratio measurement) PARAMETRIC.

correlation coefficient

measures the strength of the relationship between 2 variables. -->when r=0 there is no relationship -->when r is -1 or 1 there is a perfect correlation between variables.

Degree of Freedom

n-1

t-test

used to compare two means to see whether they could have come from the same population

Probability Value (P-value)

used to determine if differences exists between groups or conditions based on the alpha level set by the investigator. -->if p-value is less than the alpha level of 0.05 then you reject the Ho and accept the HA -->if p-value is greater than alpha level 0f 0.05 then you accept the HO and reject the HA.

post hoc tests

used to determine which specific groups or conditions are different.

linear regression equation

used to predict the value of one variable (y) based on the value of a known variable (x). y=mx+b

negative (inverse) correlation

when r is negative (0 to -1). indicates that as one variable increases the other decreases

Positive (direct) correlation

when r is positive (0 to 1). indicates that as one variable increases the other also increases