Critical Inquiry exam 2
You are given a 95% CI = .30 to .80. How is this interpreted?
95 percent of the time, our confidence interval of 0.30 to 0.80 would contain the true population mean
What are the assumptions upon which the t-test is based?
Assumption of homogeneity of variance - degree of variance will be about the same or not significantly different
What design requires the use of a two-way ANOVA?
CLINICAL INVESTIGATIONS
What is the effect size index for the t-test? What are the conventional effect sizes for small, medium and large effects?
Effect size index (d) - expresses the difference between two means in standard deviation units. May be referred to as standardized mean difference (SMD) Small: d=0.20; Medium: d=0.50; Large: d=0.80
What are the two most commonly used effect sizes indices used for ANOVA?
Eta squared (n2) and Cohen's f They represent the proportion of the total variance associated with the independent variable
What is the difference between intra-rater and inter-rater reliability?
Intra-rater reliability concerns the ability of one individual rater to be consistent from trial to trial. Inter-rater reliability concerns the ability of two or more raters to agree on ratings.
What is an effect size index?
It is a unitless, standardized value that allows comparisons across samples and studies. Ratio between effect size to variance within the data.
In performing an unpaired t-test, results of Levene's test is p = .02. Which version of the t-test will you use?
Levene's test is for equality of variances - compares the variance of the two groups. And it reports a significant difference using p (alpha level of significance). If p is less than or equal to .05 then there is too much of a difference. If p is greater than or equal to .05 then there is no significant difference, so they are the same. Then, the two tests we are looking at are equal or unequal variance t-tests. Because the variance in this scenario is significantly different then you must use the unequal variance t-test. Computers generate both automatically, so we would be using the second line in this scenario. Because Levene's test is significant, this means that the variances of the two groups are significantly different. Therefore, the second line of output is considered, "equal variances not assumed."
What is the difference between null and alternative hypotheses?
Null hypothesis - no difference between the group's they are the same Alternative hypothesis - there is a difference between groups and it is too large to be due to chance.
How many degrees of freedom are associated with the between-groups variance in a one-way ANOVA?
One less than the number of groups (k-1)
What is the difference between a one-tailed or two-tailed test?
One-tailed test is for directional hypothesis - they are more powerful and should only be used when the relevant difference is only in one direction. Two-tailed test is for non-directional hypothesis - there is a possibility that the difference may be positive or negative, don't know which way its gonna go
What are the four components involved in power analysis?
PANE Power - 1-Beta Alpha level of significance (aka p =.05) Number of subjects or sample size Effect size
What is the difference between the paired and unpaired t-test?
Paired t-test - used in repeated measures designs, when subjects are exposed to both conditions, so subjects are only compared to themselves Me 2 me Unpaired t-test - aka independent samples t-test - used when there are two groups, independent, with different subjects that are needing to be compared. me 2 you
What is the difference between a point estimate and a confidence interval?
Point estimate - single value that is obtained by direct calculation from sample data (i.e. mean) Confidence interval - range of score that is likely to contain the population parameter within a certain level of confidence (95 or 99%)
What are the three main assumptions that should be met to use parametric statistics?
Samples are randomly drawn from a parent population with a normal distribution. Variances in the samples being compared are roughly equal. Data should be measured on the interval or ratio scales.
What is sampling error?
Sampling error is the difference between a sample statistic and the analogous population parameter.
What values are used to calculate the F statistic?
So F = MSb / MSe MSb= SSb/dfb MSe=SSe/dfe MS = mean square SS = total variance (SSb and SSe ) Df = degrees of freedom (dfb = k-1 & dfe = N-k)
The results of a one-way ANOVA showed F = 4.20. The study included three groups, with a total sample of 18 subjects. What is the critical value of F associated with this test, and is it significant?
So from this we know that dfb is = 2 because (3-1) & dfe= 15 (18-3). You have to use a table that would be given to you to find the critical value of F associated with this test. Which in this case is 3.68. The F found was 4.20, it is higher, so it is significant.
What are the sources of variance in a one-way ANOVA? What are the sources of variance in a two-way ANOVA?
T-test is designed to compare two means, so if you analyze more than two means with a t-test, then you are doing it wrong. If you do this you are also more likely to make a type I error
Why is it inappropriate to use multiple t-tests to compare more than two groups?
T-test is designed to compare two means, so if you analyze more than two means with a t-test, then you are doing it wrong. If you do this you are also more likely to make a type I error
What is the purpose of the t-test?
The ratio used to compare two means. T = difference between groups/variability within groups
What are the purposes of power analysis during planning of a study and following data analysis?
There are two purposes: Estimate the sample size during planning stages of a study. Determine the probability that a type II error was committed when a study results in a nonsignificant finding.
What is the meaning of p = .02 in testing the difference between two means?
This means that there is a 2% probability that the difference between the two means occurred by chance alone. If we decide to reject H0 and say that there is a statistical difference between the two means, we have a 2% chance of being wrong.
What does the total sum of squares represent?
Total sum of squares is calculated for the combined sample around the grand mean, the total variance within the entire sample. This is split between group variance (SSb) and unexplained error variance (SSe)
What is the difference between a Type I error and a Type II error?
Type I - false-positive - mistakenly found that there was a difference between groups when in fact there was no difference. Type II - false-negative - mistakenly found that there was no difference between groups when in fact there was a difference.
What statistics are used to indicate the probability of committing a Type I or Type II error?
Type I - use alpha - which is the level of significance - aka p - standard number for p is set to .05. If you are less than or equal to .05 then there is a 5% chance that you made a type I error, this is a percentage we can live with because it is so low. Type II - use Beta and power. power is 1- beta. Power is the probability that a test will lead to rejection of the null hypothesis or the probability of attaining statistical significance. There is no standard Beta but .20 is pretty common which would be .80 power. which would translate to 80% chance that there was a difference that was not due to chance.
How are degrees of freedom determined for unpaired and paired t-tests?
Unpaired - based on sample size (N-2) (N- sample size) Paired - also based on sample size (N-1)
Why can't we accept the null hypothesis?
We cannot accept the null hypothesis because in order to do that, you would have to test the entire population in order to prove that there is absolutely no difference between the population. To truly accept that and know that it is truly zero, you would have to poll everyone. But, we can discredit the null hypothesis, or reject it, with one trial, if we find that there is a statistical significantly difference in just one sample of the population.
What are the three questions that can be asked of the data in a two-way design?
What is the effect of modality, independent of medication? What is the effect of medication, independent of modality? What is the combined effect or interaction of modality and medication?
If there is interaction between two variables, what will their relationship look like on a graph?
When there is no interaction, lines will be parallel. When there is an interaction, they will intersect, they will not be parallel, you will see that one effects the other or vice versa
What decisions can be made about the null hypothesis based on statistical findings?
Whether to -reject = statistical difference or -not reject it = no statistical difference
What statistic is used to test the variance assumption in a repeated measures ANOVA?
Within-subjects effect - difference between treatment conditions and error
