Chapter 6 - Module 11 & 12 Flashcards
What is an independent-groups t-test?
A parametric inferential test for comparing sample means of two independent groups of scores. It indicates whether the two samples perform so similarly that we conclude that they are likely from the same population, or whether they perform so differently that we conclude that they represent two different populations.
What is the standard error of the difference between means?
The standard deviation of the sampling distribution of differences between the means of independent samples in a two-sample experiment. When conducting an independent-groups t test, we are determining how far from the difference between the population means the difference between the sample means falls.
What happens when the standard error of the difference between means is large?
If the differ- ence between the sample means is large, it will fall in one of the tails of the distribution (far from the difference between the population means). Remember, our null hypothesis says that the difference between the population means is zero.
What is the logical meaning behind the standard error of the difference between two means?
The standard error of the difference between the means does have a logical meaning. If you took thousands of pairs of samples from these two populations, and found the difference between the means for each pair, those differences between means would not all be the same. They would form a distribution. The mean of that distribution would be the difference between the means of the populations and it’s standard deviation would be SX1- SX2.
What is effect size? (Cohen’s d for t-test’s)
The proportion of variance in the dependent variable that is accounted for
by the manipulation of the independent variable. Effect size indicates how big a role the conditions of the independent variable play in determining scores on the dependent variable. Thus, it is an estimate of the effect of the in- dependent variable, regardless of sample size. The larger the effect size, the more consistent is the influence of the independent variable. In other words, the greater the effect size, the more knowing the conditions of the independent variable improves our accuracy in predicting subjects’ scores on the dependent variable.
What are the levels of cohen’s d?
a small effect size is one of at least 0.20, a medium effect size is at least 0.50, and a large effect size is at least 0.80.
What is the coefficient of determination?
A measure of the proportion of the variance in one variable that is accounted for by another variable. ( we are measuring the proportion of variance accounted for in the dependent variable based on knowing which treatment group the subjects were assigned to for the independent variable)
r2= t2/ [t2 + df]
What are the levels of the coefficient of determination?
According to Cohen (1988), if r2 is at least .01, the effect size is small; if it is at least .09, it is medium; and if it is at least .25, it is large.
What will increase the size of a t-score?
Anything that increases the numerator or decreases the denominator in the equation will increase the t score.
What increases the numerator (affecting a t-score?)
A larger difference between the means for the two groups (a greater difference produced by the independent variable) will increase the numerator. This dif- ference is somewhat difficult to influence. However, if we minimize chance in our study and the independent variable truly does have an effect, then the means should be different.
What decreases the size of the denominator (in relation to the t-score)
Because the denominator is the standard error of the difference between the means (sX1 - X2) and is derived by using s (the unbiased estimator of the population standard deviation), we can decrease sX1 - SX2 by decreasing the variability within each condition or group or by increasing sample size.
In summary, what are three aspects of a study that can increase power in a t-test?
- Greater differences produced by the independent variable.
- Smaller varaibility of raw scores in each condition.
- Increased sample size.
power = d (square root of n/2)
Assumptions of the Independent T-test:
- The data is interval-ratio scale
- The underlying distributions are normal
- The observations are independent
- Homogeneity of variance If we could compute the true variance of the
population represented by each sample, the variance in each population would be the same.
If violated - use another stat. Example:
If the scale of measurement is not interval-ratio or if the underlying distribution is not normal, it may be more appropriate to use a nonparametric stat.
If the observations are not independent, then it is appropriate to use a dependent t-test.
CRITICAL THINKING MODULE 11 - QUESTION 1: how is effect size different from significance level? In other words, how is it possible to have a significant result, yet a small effect size?
The effect size indicates the magnitude of the experimental treatment regardless of sample size. A result can be statistically significant because sample size was very large, but the effect of the independent variable was not so large. Effect size would indicate whether this was the case, because in this type of situation the effect size should be small. (Because effect size of the IV was small therefore the effect size should be small)
CRITICIAL THINKING MODULE 11 - QUESTION 2: How does increasing sample size affect a t test? Why does it affect it in this manner?
In the long run it means that the calculated t is more likely to be significant. This is so because in terms of the formula used to calculate t, increasing sample size will decrease the standard error of the difference between means (sX1 - X2). This in turn will increase the size of the calculated t, which means that it is more likely to exceed the critical value and be significant.
