(Quantitative): Comparing groups: continuous variables

Question 1

What is statistical data analysis?

Answer 1

• Organise and analyse the data
• Common procedures used in analysis:
 -Descriptive Statistics
 - Inferential Statistics (more of a focus this term)
 • Need to get data into shape

Question 2

What does data analysis need to do/have?

Answer 2

• Needs to have a purpose
• Describe
• Compare
• Examine similarities
• Examine differences

Question 3

What is descriptive statistics (recap from last semester)?

Answer 3

• Check for errors and outliers
• Describe & summarise
• Spread of the data
• Ensure appropriate analysis
• Data parametric or non‐parametric

Question 4

What ways can data be summarised (ratio or interval)?

Answer 4

• Measure of Central Tendency
  -Mean, Median, Mode
  - If not normal‐median
• Measure of Dispersion
 -Variation, Range, Standard Deviation
• Normal Curve, Skewness, Kurtosis

Question 5

What are inferential statistics?

Answer 5

All statistical tests of common structure:
• Set up a null and alternative hypothesis
• Establish a level of statistical significance (also known as alpha (α), usually set at 5% or 1%)-depends on study
• Determine statistical significance of the findings‐ p value
• Accept or reject the null hypothesis-is there a difference between two groups
- SPSS output provides a p‐value (probability value)
- If the p‐value is greater than the alpha you cannot reject the null hypothesis
note:may be statistically significant but not actually meaningful e.e.g 1 second difference in a marathon

Question 6

What are the steps when undertaking a hypothesis test?

Answer 6

• Define study question
• Set null and alternative hypothesis
• Calculate a test statistic
• Calculate a p value
• Make a decision and interpret

Question 7

What is the students t-test?

Answer 7

• The t‐test is used to compare means between groups
• t‐test is easy to use but can be easily misused
• Most common statistical procedure used by researchers

Question 8

What are the two types of t-test?

Answer 8

Same principles behind each but there is more random error in the …
• INDEPENDENT SAMPLES DESIGN because the control
group might, by chance, be very different from the treatment group
• With the PAIRED DESIGN, each person is their own control so variation is limited

Question 9

What is the process in the decision chart for bivariate data?

Answer 9

• Paired data–>Paired samples t-test–>wilcoxon signed rank test (for non-parametric)
• Independent data–>Independent samples t-test–>Mann Whitney u-test (for non-parametric)

Question 10

What is independent data?

Answer 10

• Data comes from different (independent) groups of people
• Eg. classic experiment (eg. Group 1 receives intervention A,
Group 2 receives intervention B).
• Study participant is in one group only
• Compare differences between groups (mean or median)

Question 11

What is paired data?

Answer 11

• Data comes from one group of individuals
• Data collected from an individual at different points in time or under different conditions
• Compare differences in outcome between time 1 and time 2 or condition 1 and 2 (mean or median)
• Other terms: repeated measures, before and after study
e.g. cycling speed with different helmets

Question 12

Explain the independent samples design

Answer 12

• Dependent Variable is ratio/interval and Independent Variable has two categories
• Measurements in condition 1 are independent of
measurements in condition 2
• If the H0 is true we expect the difference between the mean of condition 1 group and condition 2 group to be zero

Question 13

Explain the issue of error in an independent t-test

Answer 13

• The act of using a sample will introduce error
-What is the probability that the difference we found occurred by chance?
-If less than 5%, reject H0 and accept HA (or written H1
‐ alternative)

Question 14

Explain the sampling distribution of the independent samples t-test?

Answer 14

• T-distribution shape similar to normal curve
• the middle is the population parameter when H0
is true (i.e. the mean difference is 0)
• Around it are all the possible sample statistics
• Is ‘our’ difference so big that would only rarely happen by chance?
- Rarest 2.5% in both tails

Question 15

What are the assumptions for the independent samples t-test?

Answer 15

• Dependent Variable is ratio/interval
• If either group is small (30 or less), distribution of Dependent Variable for each group should not be badly skewed
• The variance of the Dependent Variable for the two groups should not be very different

Question 16

How is a problematic difference indicated in an independent t-test?

Answer 16

• A problematic difference in variances is indicated by a significant Levene’s Test:

• If significant, interpret the p value associated with ‘equal variances not assumed’
• If non‐significant, interpret p value associated with ‘equal variances assumed’

Question 17

What about paired data that is normal? (check)

Answer 17

• Observations not independent
• Paired equivalent‐ Paired sample t test (same assumptions)
• H0: No difference in the means before and after
• H1: A difference in the means before and after

Question 18

Explain the paired samples t-test design

Answer 18

• Dependent Variable is ratio/interval and Independent Variable has two categories
• Each measurement in Cond 1 (performance with caffeine) has a match in Cond 2 (performance with water)
• One measurement is deducted from the other so that each case has a different score
• If the null hypothesis (H0 ) is true and there is no difference in performance with e.g. caffeine and with water we would expect the group mean difference score to be 0

Question 19

Explain the issue of error in a paired-samples t-test

Answer 19

the act of using a sample will introduce error
• What is the probability that the difference we found occurred by chance?
• If less than 5%, reject H0 and accept HA
(or written H1 ‐ alternative)

Question 20

What would non-parametric equivalents to a t-test be used?

Answer 20

• If we have an ordinal scale Dependent Variable, or a ratio/interval Dependent Variable that does not meet parametric assumptions we use non‐parametric equivalents
• These compare medians (ranks) (not affected by extremes) rather than means
• They are usually less powerful

Question 21

When should non-parametric tests be used?

Answer 21

• used when assumptions of parametric tests are not met (i.e. breached) e.g. the level of measurement (e.g., interval or ratio data), normal distribution, and homogeneity of variances across groups
• It is not always possible to correct the distribution of a data set
• In these cases we have to use non‐parametric tests
• They make fewer assumptions about the type of data on which they can be used
• Many of these tests use “ranked” data

Question 22

But what if my data are independent but nonparametric?

Answer 22

• Mann‐Whitney U test e.g. income ranks between teams

Question 23

What is the mann-whitney u-test

Answer 23

• It is used to test the null hypothesis that two samples come from the same population (i.e. have the same median)
• or, alternatively, whether observations in one sample tend to be larger than observations in the other

Question 24

What are the assumptions of the mann whitney u-test?

Answer 24

• (also known as the Mann‐Whitney U) is similar to the two independent samples t‐test
• Data must meet the requirement that the two
samples are independent
• The Mann‐Whitney procedure uses ranks instead of
the raw data values
• Data values are assigned ranks relative to both
samples combined

Question 25

When should a mann-whitney u-test be used?

Answer 25

• The sample sizes are small and normality is questionable.
• The data contain outliers or extreme values that, because of their magnitude, distort the mean values and affect the outcome of the comparison.
• The data are ordinal
• Assumes distributions of two groups being compared are the same shape
• Assumes not too many ties in ranks of data

Question 26

What is used for paired non-parametric?

Answer 26

• The Wilcoxon Signed‐Rank test or sign test
• Can use interval, ratio or ordinal data
• Null hypothesis the same as for Mann‐Whitney U test
but for paired data

Question 27

Explain the Wilcoxon signed-rank test

Answer 27

• The Sign test can be used to measure the differences between each variable as nonparametric alternatives to the one sample t‐test
• The Wilcoxon Signed‐Rank test can be used to compare paired data as nonparametric alternatives to the paired t‐test
• These tests are used when you cannot justify a normality assumption for the differences
• The sign test is very simple in that it counts the number of differences that are positive (+) and those that are negative (‐) and makes a decision based on these counts

Question 28

Give examples of paired and independent data?

Answer 28

Paired: Cyclicling rate difference between people within a company
Independent: comparing cycling rates across companies

Question 29

Explain the process of hypothesis testing

Answer 29

All statistical tests of common structure:
• Set up a null hypothesis
• Establish a level of statistical significance (also known as alpha (α), usually set 5% or 1%)
• Determine statistical significance of the findings
• Accept or reject the null hypothesis
• SPSS output provides a p‐value (probability value)
• If the p‐value is greater than the alpha you can accept
the null hypothesis

Question 30

Explain the p-values

Answer 30

• The p value quantifies the chance of observing such a
value of the test statistic (or one more extreme) if the
null hypothesis was actually true
• If set an Alpha level of .05 (5%) then you decide to
reject H0 and accept HA when p is no more than .05
• This leaves up to 5% chance that you are wrong in
concluding that there is a difference (making a Type 1
error)

Question 31

What are type 1 and 2 errors?

Answer 31

• Type I Error is the rejection of a null hypothesis when it is true. (This probability is known as significance level of test usually at 5% or 1% and decided before the test is conducted. (false posiitve) e.g. tell a man they’re pregnant
• Type II Error is the failure to reject the null hypothesis, which is false. (false negative) e.g. tell a preganant woman they a not pregnant

Question 32

What are some limitations of independent t-tests?

Answer 32

• Doesn’t take into the impact of population size on the chances of type 1 error

Question 33

What does the Levene’s test?

Answer 33

Homogeneity of variances

Question 34

what does 0.000 tend to mean in spss?

Answer 34

<0.001