Statistics and Data Analysis in Quantitative Study Designs

Question 1

What are the levels of measurement/types of data?

Answer 1

Nominal, ordinal, interval, ratio
Each level has an additional characteristic, and contains all of the characteristics of the previous level.
Nominal and ordinal contain non-parametric data.
Interval and ratio contain parametric data.

Question 2

Nominal

Answer 2

Provides information about difference, but not much more.
Used to name identify, or classify into categories.

Question 3

Ordinal

Answer 3

Shows direction of difference, but we don’t know amount of difference.
Numbers indicate rank or order.
Allows for greater than or less than.

Question 4

Interval

Answer 4

Intervals or distances between numbers are known, but it’s not known how far any of the numbers are from zero.
Equality of units, but no true zero.

Question 5

Ratio

Answer 5

Each number can be thought of as a distance measured from zero.
There is an absolute zero point, which represents the absence of the variable being measured.

Question 6

Statistics

Answer 6

Objective means of interpreting data
Inform people about reliability and meaningfulness.
Measures of central tendency and variability are the most fundamental components of most statistical techniques.

Question 7

Central Tendency

Answer 7

Attempts to describe a set of values by placing focus on the central position in the data set.
A single score.
Measures of central tendency include mean, median, mode.

Question 8

Mean

Answer 8

The sum of all scores in a data set, divided by the number of scores in the data set.
The average.
The most common measure of central tendency.
The mean can be effected by outliers (skews data depending on if the outlier is higher or lower than the rest of the data).

Question 9

Median

Answer 9

The number occurring at the midpoint of the data set.
If there is an even number in a data set, take the mean of the two mid-point scores.
Not affected by skewed data.
Drawback is that median may not represent all data.

Question 10

Mode

Answer 10

The most frequently occurring number in a data set.
Mode is the most popular option (see frequency of a number)
Drawback is that 2 modes or no two of the same responses (can get 2 modes)

Question 11

Variability

Answer 11

Best estimate of the spread of scores.
Indicates how spread out the scores are or how close they are to the mean.
If variance = 0, all values in the data set are the same.
If variance is low, the values are close to the mean and the range is small.
If variance is high, the range of values is vast and some of the values are far from the mean.

Question 12

Standard Deviation

Answer 12

Is the square root of the variance.

Question 13

Normal Distribution

Answer 13

Many statistical tests are based on the assumption of a normal distribution.
Distributions provide a visual way to see scores disperse from the mean.
Normal distributions are symmetrical around the mean.
Graph of distributions found in notes on statistics.

Question 14

t-Test

Answer 14

Comparing means.
If comparison is focused on two groups/samples, the appropriate stat is a t-test.
Aims to understand the difference between the means of those two groups.
Groups may be different or same people measured twice.
Includes independent t-test and dependent t-test.

Question 15

Independent t-test

Answer 15

Used when the study has two groups of different participants
Can be used for experimental and quasi-experimental designs.
Compare two independent samples.

Question 16

Dependent t-test

Answer 16

When two data points collected over time or when participants are exposed to the two experimental conditions.
Compare scores from same or matched sample.

Question 17

What happens where there are more than two groups/samples that are different?

Answer 17

One way ANOVA (extension of t-test).
Can include repeated measure (repeated measure ANOVA is used when two different time points or more).

Question 18

What happens after finish statistical analysis?

Answer 18

We revisit the hypothesis.

Question 19

P-values

Answer 19

Probability of error = p-value
Researchers aim to reduce chances of error as much as possible.
P-values of 0.05 means there is 5% room for error or chance (researchers are also 95% confident that the results are genuine and not a chance finding).
Written in research p less than 0.05 = significance or ability to reject the null hypothesis.

Question 20

Type I Error

Answer 20

Researchers make the decision that a manipulation or treatment has been successful when it in fact has not been.

Question 21

Type II Error

Answer 21

Researchers make the decision that the manipulation has failed when it worked.

Question 22

What are some other types of distribution?

Answer 22

Skewness: scores spread out more at one end of the distribution (positive or negative).
Kurtosis: peakedness of distribution.

Question 23

Correlation

Answer 23

A measure of the strength of the relationship between two variables (x and y).

Question 24

Pearson product-moment correlation

Answer 24

Assumes x and y are normally distributed and are interval or ratio scale scores.
Pearson r

Question 25

Spearman rank-order correlation

Answer 25

Used for ordinal scale data or interval or ratio scale data that deviate substantially from normality.

Question 26

Pearson r

Answer 26

Pearson r is a relationship independent of number of scores, size of scores, dispersion of scores.
Pearson r is derived from covariance.

Question 27

What information can you get from Pearson r?

Answer 27

Direction of relationship: positive correlation means x increases and y increases; negative correlation means x increases and y decreases or vice versa.
Strength of the relationship: closer to line/mean = stronger relationship

Question 28

Correlation Coefficient

Answer 28

A measure of the direction or strength of a linear relationship (relationship shown from Pearson r).
Can be positive (closer to 1.0) or negative (closer to -1.0).
Can also be no relationship (closer to 0.0).

Question 29

What is the significance of r in a correlation?

Answer 29

Significant correlations do NOT provide the basis for drawing causal conclusions.
Causation depends on methodology, not analysis.

Question 30

Null Hypothesis

Answer 30

The observed correlation is due to error.

Question 31

Alternative Hypothesis

Answer 31

There will be a significant correlation between x and y