Psych 300A: Final Review (Single Sample t Tests)

What is the major problem regarding z scores for hypothesis testing

We need to known the population parameters to participate in hypothesis testing which is often not known

How can we estimate mu and sigma

Mu - estimate using the sample mean, poses no additional problems

Sigma - estimate using the s of the sample, leads to sigma being underestimated

How do we calculate s

Same way as SD but replace N with N - 1 for the denominator

Degrees of freedom

Number of scores in a sample that are independent and free to vary

df = N - 1 in a single sample design

Estimated standard error

Used to estimate the population standard error when the value of sigma when sigma is not known

𝑠x̄ = s / √N

t statistic

Statistic used to test hypotheses about a population mean when the value of sigma is unknown

Calculated the same way as z but swap out the denominator with 𝑠x̄

How is t represented theoretically

(mean) - (mean of sampling distribution) / (estimated standard error)

OR

(explained variability) / (unexplained variability)

What 2 conditions must be met to use a t test

1. We have scores for one sample of individuals

2. We want to compare this sample with a population where SD is unknown

T or F: When we estimate z from t they are always equal

F, not necessarily equal

T or F: The greater the degrees of freedom the better the s and sx represent the population and distribution statistics

T, also leads to the t distribution being more closely approximated to SND

T distribution

Complete set of values for every possible random sample for a specific sample size (n) or specific degrees of freedom (df)

What is the range, shape, central tendency and variability of the t-distribution

Value Range - (-∞, ∞)

Shape - kurtotic, but as df approaches infinity the t-dist approximates to SND

Central tendency - mean = 0

Variability - more variable (flatter) than SND

How do we get the tcrit using a t-table

Use df and a as well as the direction our test, table outputs a t score

What do we do if df is not in the table

Use the most closely related df that is less than the df we have (e.g. if we have 85 use df = 80)

When must we use a t-test compared to a z-test

When the population statistics are unknown (typically sigma)

What are the 4 assumptions we make when engaging in a t-test

1. Sample participants are randomly sampled from population

2. Behaviour we study (DV) is normally distributed in population or n ≥ 25-30 (so we can assume normal distribution)

3. Data is on an interval/ratio scale

4. N ≥ 7 (small sample size can lead to inability to reject the null)

T or F: When reporting our results we always need a baseline

T, in single participant and single sample designs a baseline is always needed