Biological Psychology: Hypothesis Testing

Flashcards covering the fundamentals of statistical hypothesis testing, experimental designs, the t-distribution, and the procedures for conducting one-sample t-tests.

Why can we not draw conclusions about a population solely from two sample means?

Because we do not know if the difference is real or due to chance factors such as measurement error or a small sample size that does not represent the full population.

What is the function of a 'chance distribution' in statistical testing?

It represents the null hypothesis ($H_0$), assuming the real difference to the baseline is $0$, allowing researchers to determine how likely their empirical result was under the assumption of chance.

Why is a t-distribution used instead of a z-distribution in most psychological research?

A z-distribution requires knowing the population standard deviation, which is usually unknown; the t-distribution uses an estimate of the standard error based on the sample.

How does the shape of the t-distribution change according to the degrees of freedom ($df$)?

The distribution looks broader for lower degrees of freedom ($df$) and becomes more like a normal distribution as the degrees of freedom ($df$) increase.

Define a one-sample experimental design.

A design where a single group mean is compared to a specific known value, such as a known population mean (e.g., comparing a group's IQ to the population average of $100$).

What is a between-groups (independent-measures) design?

A design featuring two separate groups where the values come from different people, meaning each participant provides only one measure for one group.

What are the primary disadvantages of a between-groups design?

Participants in different groups may differ in personality or motivation; large sample sizes or counterbalancing are required to average out these individual differences.

Define a within-group (repeated-measures) design.

A design where a single group provides data for multiple conditions, meaning the values in each condition come from the same participants.

What is an advantage of the repeated-measures design regarding baseline factors?

It controls for differences in baseline factors like personality because those factors affect both experimental conditions equally.

What is the formula for the t-statistic in a one-sample t-test?

$t = \frac{M - \mu}{s_M}$, where $M$ is the sample mean, $\mu$ is the population mean, and $s_M$ is the estimated standard error of the mean.

How is the estimated standard error of the mean ($s_M$) calculated?

$s_M = \frac{s}{\sqrt{n}}$, where $s$ is the sample standard deviation and $n$ is the sample size.

What is the formula for degrees of freedom ($df$) in a one-sample t-test?

$$df = n - 1$$

How is the variance ($s^2$) calculated using the Sum of Squares ($SS$)?

$$s^2 = \frac{SS}{df}$$

What is the difference between a directional and a non-directional hypothesis?

A non-directional hypothesis ($H_1: \mu \neq 10$) predicts any difference, while a directional hypothesis (H_1: \mu > 10 or H_1: \mu < 10) predicts a specific direction of the effect.

When is a two-tailed test usually preferred over a one-tailed test?

If there is doubt about the direction, or if missing an effect in the opposite direction would be negligible, unethical, or irresponsible (e.g., testing if a new treatment is less effective than the standard).

What does a high variance do to the results of a t-test?

Increased variance increases the error term, resulting in a lower empirical t-value ($t_{empirical}$), which makes it less likely to find a significant result.

Does a larger t-value indicate a stronger effect size?

No; the t-value itself does not quantify effect strength. Effect size measures like Cohen's $d$ or $r^2$ must be calculated separately.

Why is variance calculated by dividing Sum of Squares ($SS$) by $n - 1$ instead of $n$?

This provides a measure of deviation that is independent of sample size, allowing for the comparison of deviation across samples of different sizes.