Lecture 6 - Independent Samples T-Test. T-Statistics. Hypothesis Testing. Box Plots.

Question 1

Which statistic tells us about the variability in our sample?

Answer 1

The standard deviation

Question 2

Estimations of means and mean differences are more accurate when sample sizes are ______ and standard deviations are _______.

Answer 2

Estimations of means and mean differences are more accurate when sample sizes are LARGER and standard deviations are SMALLER.

Question 3

Which statistic encapsulates the sample size and the standard deviation?

Answer 3

The standard error of the mean.

σ ∕ √N

Question 4

We expect greater accuracy in estimation when the SE of the mean is _________.

Answer 4

We expect greater accuracy in estimation when the SE of the mean is SMALLER.

Question 5

A difference is bigger when the mean differences are ______ and standard deviations are _______.

Answer 5

A difference is bigger when the mean differences are GREATER and standard deviations are SMALLER.

Question 6

Which statistic encapsulates the mean difference and the standard deviations in a sample?

Answer 6

The effect size.

d = M1 - M2 / SD

Question 7

Which statistic encapsulates the sample size, the mean difference, and the standard deviations?

Answer 7

The T-Statistic

One Sample t = x̄ - μ / SE

Related Samples t = x̄1 - x̄2 / SE

Independent Samples
t = x̄1 - x̄2 / √ (Ssq1 / N1) + (Ssq2 / N2)

sq = squared (sorry, can’t seem to copy the superscript 2!)

Question 8

What does a greater magnitude (large positive or large negative) of t-value indicate?

Answer 8

Stronger evidence of a difference

Question 9

On a t-distribution, which areas under the curve represent the p-value?

Answer 9

The areas from the t-statistic and more extreme on both sides of the distribution.

Question 10

Which statistics are represented in a box and whisker diagram?

Answer 10

Median, Range, Highest and Lowest Observations, Quartile 1 (Lower Q) and Quartile 3 (Upper Q)

You can also see the general distribution of the scores ie whether the data are symmetrical or skewed.

Question 11

Which 3 things do you need to cover when reporting the results of a t-test?

Answer 11

1. DIRECTION: How do the groups compare using directional words? eg Group A was faster than Group B, Group A was shorter than Group B.
2. MAGNITUDE: Descriptive statistics - Means, SD, Effect Size (cohen’s d)
3. SIGNIFICANCE: Inferential Statistics - T-Test results t(df)=0.00, p=.000 and the decision/conclusion

Question 12

If the t-value is larger, the difference between the means is ________.

Answer 12

Larger.

Question 13

If the t-value is larger, the standard error of differences between the means is ________.

Answer 13

Smaller.

Question 14

The t-value is larger if the standard deviation of the samples is ______.

Answer 14

Smaller.

Question 15

The t-value is larger if the sample size is _______.

Answer 15

Larger.

Question 16

How does the df affect the p-value?

Answer 16

The same t-value for a group with a higher df will result in a smaller p-value.

Question 17

Why do we use a t-test?

Answer 17

The t-test is used to determine whether we have enough evidence of a difference in our sample data.

Running a t-test gives us a probability (p-value) that we can use as evidence of whether or not there is a mean difference.