Statistics Ch. 11 Clarifying the concepts

EHy does effect size use standard deviation rrather than standard error

The effect-size calculation uses standard deviation because sample size is not used in the calculation of this measure of variability.

When is it appropriate to use the independent samples t test

An independent-samples t test is used when we do not know the population parameters and are comparing two groups that are composed of unrelated participants or observations.

What is the difference between s2x and s2y

Both of these represent corrected variance within a group (s2), but one is for the X variable and the other is for the Y variable. Because these are corrected measures of variance, N - 1 is in the denominator of the equations.

How do we interpret effect size using cohens d

Guidelines for interpreting the size of an effect based on Cohen's d were presented in Table 11-2. Those guidelines state that 0.2 is a small effect, 0.5 is a medium effect, and 0.8 is a large effect.

Why might we want to transform our data

If the distribution of the sample data is skewed, we may want to transform the data to eliminate skew so that we can use parametric hypothesis tests, such as independent samples t test, which assume a normal distribution for the population.

What are independent effects

Independent events are things that do not affect each other. For example, the lunch you buy today does not impact the hours of sleep the authors of your book will get tonight.

How does the size of our confidence interval relate to precision of our prediction

Larger ranges mean less precision in making predictions, just as widening the goal posts in rugby or in American football mean that you can be less precise when trying to kick the ball between the posts. Smaller ranges indicate we are doing a better job of predicting the phenomenon within the population. For example, a 95% confidence interval that spans a range from 2 to 12 is larger than a 95% confidence interval from 5 to 6. Although the percentage range has stayed the same, the width of the distribution has changed.

What is pooled variance

Pooled variance is a weighted average of the two estimates of variance—one from each sample—that are calculated when conducting an independent-samples t test.

Explain random assignment and what it controls

Random assignment means that all participants have an equal chance of being assigned to each level of the independent variable. Random assignment should, in theory, result in an equal distribution of many phenomena (e.g., height, weight, intelligence, age) across the different conditions. By distributing these factors across the levels of the independent variable, they are held constant and should not impact the effect of an independent variable of interest on a dependent variable.

As they relate to comparison distributions, what is the difference between mean differences and differences between the means

The comparison distribution for the paired-samples t test is made up of mean differences—the average of many difference scores. The comparison distribution for the independent samples t test is made up of differences between means, or the differences we can expect to see between group means if the null hypothesis is true.

Explain how the paired samples t test evaluates individual differences and the independent samples t test evaluates group differences

The paired-samples t test involves comparing individual scores across two conditions. In Chapter 10, the example used was weight before and after a holiday break in college. Each individual's weight was compared across these two times, creating individual difference scores. For the independent samples t test, the behavior of an entire group is compared to that of another group. One example used in this chapter was percentage of cartoons considered to be humorous by men versus women. Scores for the individuals within a group are averaged together and compared to the average for the other group.

What does the square root transformation do to the distribution of the data

The square root transformation compresses both the negative and positive sides of a distribution.

As a meaure of variability what is the difference between standard deviation and variance

Variability can be measured several ways, including variance and standard deviation. Both measures can give us a sense of the average distance that scores are away from the mean. Variance is expressed in squared units, whereas standard deviation returns the measure back to the original units by taking the square root of variance.

What is the difference between pooled variance and pooled standard deviation

Variance is the standard deviation squared. This is the only difference between pooled variance and pooled standard deviation.

Why should we want the variability estimate based on a larger sample to count for more than the smaller sample

We assume that larger samples do a better job of estimating the population than smaller samples do, so we would want the variability measure based on the larger sample to count more.

How do confidence intervals relate to margins of error

We can take the confidence interval's upper bound and lower bound, compare those to the point estimate in the numerator, and get the margin of error. So, if we predict a score of 7 with a confidence interval of [4.3, 9.7], we can also express this as a margin of error of 2.7 points (7 ± 2.7). Confidence interval and margin of error are simply two ways to say the same thing.

Define the symbols

s2difference is the variance of the distribution of differences between means, which is the sum of the variance versions of standard error for each sample, 〖s^2〗_(M_(X ) ) and 〖s^2〗_(M_(Y ) ).