## constructing confidence interval given paired data

To use paired data to construct a confidence interval, the following conditions must be met.

``````All possible samples of a given size have an equal probability of being chosen; that is, simple random samples are used.

The samples are dependent.

Both population standard deviations, σ1
``````

and σ2

are unknown.

Either the number of pairs of data values in the sample data is greater than or equal to 30
(n≥30)

``````or the population distribution of the paired differences is approximately normal.
``````

In this lesson, you may assume that these conditions are met for all examples and exercises involving paired data.

The value that we want to estimate is the mean of the paired differences for the two populations of dependent data, μd
. Recall that the first step in constructing a confidence interval is to find the point estimate, and the best point estimate for a population mean is a sample mean. Therefore, the mean of the paired differences for the sample data, d⎯⎯

is the point estimate used here.

Formula: Mean of Paired Differences

``````When two dependent samples consist of paired data, the mean of the paired differences for the sample data is given by

d⎯⎯=∑din
``````

where di

is the paired difference for the ith pair of data values and

n is the number of paired differences in the sample data.

## Understanding oneway repeated Measures Designs

Qn1. What primarily distinguishes a oneway repeated measures ANOVA from a one-way ANOVA?

``````- The presence of multiple factors
- The presence of a between-subjects factor.
- The presence of a within-subjects factors.
- None of the above
``````

Qn2. All else being equal, which of the following is a reason to use a within-subjects factor instead of a between-subjects factor?

``````- The data is more reliable
- The data exhibits less variance
- The factors are easier to analyze
- The exposure to confounds is less
- Less time from each subject is required
``````

Qn3. In a repeated measures experiment, why should we encode an Order factor and test whether it is statistically significant? (Mark all that apply)

``````- To examine whether the presentation order of conditions exerts a statistically significant effect on the response.
- To examine whether any counterbalancing strategies we may have used were effective
- To examine whether confounds may have affected our results
- To examine whether our factors cause changes in our response
- To examine whether out experiment discovered any differences``````

Qn4. How many subjects would be needed to fully counterbalance a repeated measures factor with four levels?

`` - 4,8,16,24,32``

Qn5. For an even number of conditions, a balanced Latin Square contains more sequences than a Latin Square.

``````- True
- False``````

Qn6. For a within-subjects factor of five levels, a balanced Latin Square would distribute which of the following number of subjects evenly across all sequences?

``````5, 15, 20,25,35
``````

Qn7. Which is the key property of a long-format data table?

``````- Each row contains only one data point per response for a given subject.
- Each row contains all of the data points per response for a given subject.
- Each row contains all of the dependent variables for a given subject.
- Multiple columns together encode all levels of a single factor.
- Multiple columns together encode all measures for a given subject``````

Qn8. Which is not a reason why Likert-type responses often do not satisfy the assumptions of ANOVA for parametric analyses.

``````- Despite having numbers on a scale, the response is not actually numeric.
- Responses may violate normality
- The response distribution cannot be calculated
- The response is ordinal
- The response is bound to within, say, a 5- or 7-point scale.
``````

Qn9. When is the Greenhouse-Geisser Correction necessary?

``````- When a within-subjects factor of 2+ levels violates sphericity
- When a within-subjects factor of 2+ levels exhibits sphericity
- When a within-subjects factor of 3+ levels violates sphericity
- When a within-subjects factor of 3+ levels exhibits sphericity
- None of the above
``````

Qn10. If an omnibus Friedman test is non-significant, post hoc pairwise comparisons should be carried out with Wilcoxon signed-rank tests

``````-True
-False
``````