Research Methods 1 - 5. Confidence Intervals for the Mean

How can you use a sample mean to estimate the location of the population mean?

A population mean is a fixed point on a number line. The mean of a sample drawn from that population will also fall on that number line. We do not know exactly where the sample mean will be in relation to the population mean but we know where it is likely to be from the standard error of the mean and from the shape of the sampling distribution of the mean. This is the purpose of the confidence interval = an interval around the sample mean that has a specified chance of including the population mean.

What are the 3 kinds of differences between means?

1. One-sample differences = interested in the means of one sample of scores.

2. Related-samples difference = interested in two means for two samples of scores from the same source, there is no way to pair up the scores.

3. Independent-samples differences = interested in two means for two samples of scores from different sources, there is no way to pair up the scores.

What does the width of a confidence level depend upon?

The standard error of the mean (which is calculated from the standard deviation and sample size).

E.x: Calculate the width of a 95% Cl.

1. We want to know on the NDC the extent that includes the middle 95% of values. Therefore, we halve the remaining 5% into 2.5% on each tail.

2. 2.5% as decimal would be 0.0250.

3. We take this value of 0.0250 and refer to the NDC table in order to find the multiplier value with the smaller portion of 0.0250 = 1.96

What is the formula to calculate the standardised effect size for mean difference/Cohen's d?

the difference between the two population means / standard deviation of either population

What is the formula to estimate the effect size for a mean difference from sample data?

difference between the two sample means / estimate of within-population standard deviation

What does estimating the effect size for a mean difference from sample data tell us?

How much the two samples of scores overlap. When there is a large effect size, there is less overlap.

As a general rule, what size of mean difference do psychologists label as small, medium, and large?

Small = 0.2

Medium = 0.5

Large = 0.8

Which standard deviation do you use for effect size (when there is a choice)?

- Ideally, we would use the population standard deviation, but this is rarely known.

- If there is a control/baseline group = use the standard deviation for this group.

- If there is no control group = combine/pool the two samples of data and use the average (pooled) variance to obtain a single standard deviation.

Average (pooled) variance = (SD1 + SD2) / 2

SD using pooled variance = the square root of the average (pooled) variance

E.x: Mean (SD) memory span is 6.81 (1.57) for digits and 4.40 (1.25) for words.

1. Mean difference = 6.81 - 4.40 = 2.41

2. Pooled variance = (1.57 + 1.25) / 2 = 1.41

3. SD from pooled variance = the square root of 1.41

4. Effect size (Cohen's d) = 2.41 / 1.41 = 1.70