Comparing means and proportions Flashcards
If the value is more than 0.05 is this value significant statistically?
If its bigger than 0.05 it is NOT statistically significant.
If it is less than 0.05 it is statistically significant
Is 0.67 significant?
No - more than 0.05
Is 0.003 significant?
Yes - less than 0.05
If data is categorical, what are the 3 types of test we would carry out?
One sample X2 test - one sample
Pearsons chi-square test - two independent samples
McNemar test - two paired samples
If data is numerical, what are the 3 types of test we would carry out?
One sample t-test
Independent sample t-test
Paired sample t-test
What is the symbol for the ‘known population’
U0
When we conduct a test to compare means or proportions, we use the result to work out if we can reject the null hypothesis or not. How?
Compare against the P value, if less than 0.05 it is significant, if it is above 0.05 then it is not statistically significant
With this hypothesis, what test would we use?
H0: μ=μ0
Ha: μ≠μ0
Is the population mean (μ) equal to a certain value (μ0) ?
One Sample T-test
With this hypothesis, what test would we use?
H0: π=π0
Ha: π≠π0
Is the population proportion (π) equal to a certain value (π0) ?
One sample X2 test
With this hypothesis, what test would we use?
H0: μA=μB
Ha: μA≠μB
In the population, is the mean of group A (μA) equal to the mean of group B (μB) ?
Two Independent samples t-test
With this hypothesis, what test would we use?
H0: πA=πB
Ha: πA≠πB
In the population, are the proportions for each group (πΑ & πΒ) equal across the categories of the characteristic?
Pearsons chi-squared test
With this hypothesis, what test would we use?
H0: μ1=μ2
Ha: μ1≠μ2
In the population, is the mean of a group in one condition (μ1) equal to the mean of the same (or
paired) group in another condition (μ2) ?
Two paired samples t-test
With this hypothesis, what test would we use?
H0: π1=π2
Ha: π1≠π2
In the population, are the proportions for each group (π1 & π2) equal before and after?
McNemar test
What is meant by parametric test?
Parametric testsas the sample mean is an estimator of a population parameter
Give an example of…
a. one sample
b. independent sample
c. paired sample
a. Do prisoners have more divorced parents?
b. Do prisioners in the USA have more divorced parents than prisioners in the UK
c. Does sleeping pills make someone sleep better?
Who came up with the 3 t-tests?
William S. Gosset
What are the three main assumptions we must have before conducting a one sample t-test?
- The observations are randomly and independently drawn
- There are no outliers
- Symmetrical data (approximately normally distributed)
When interpreting the one sample t-test SPSS table what values do we need to look at?
The test value and the mean difference value. We look at the p-value to see if it is a significant finding. We also report the t value, df and CI
What are the three main assumptions we must have before conducting a two independent sample t-test?
The observations are randomly and independently drawn
• Symmetrical data, within each group
• There are no outliers, within each group
When interpreting the independent sample t-test SPSS table what values do we need to look at?
Need to look at the Levene test to see if the p value is significant. If it is significant, then we use the second/bottem line of the SPSS table. If it is not significant then we use the top line. We report the mean difference, t value, CI, P value and DF
What are the three main assumptions we must have before conducting a paired sample t-test?
The (paired) observations are randomly and independently drawn
• The (paired) difference are is symmetrical continuous variable
• There are no outliers in the difference
When interpreting the paired sample t-test SPSS table what values do we need to look at?
Look at the mean and the P value. We need to report the t value, CI, P value and DF
What are the three main assumptions we must have before conducting a one sample chi-square (X2) test?
• The observations are randomly and independently drawn
- The number of cells with expected frequencies less than 5, are less than 20%
• The minimum expected frequency is at the very least 1.
When interpreting the one sample chi-squared table what values do we need to look at?
SPSS prints a table with descriptive statistics and one with the one sample t-test.
We report the X2 value, df and p-value (this is the asymp. sig)
We need to make sure the cell expected frequency is below 20% and the minimun expected frequency needs to be larger than 1
What did Karl Pearson invent?
Pearsons chi-square test
What are the four main assumptions we must have before conducting the pearsons chi-square test?
- The observations are randomly and independently drawn
- The number of cells with expected frequencies less than 5, are less than 20%
- The minimum expected frequency is at the very least 1.
- The observations are not paired
When interpreting the pearsons chi-square test table what values do we need to look at?
- SPSS prints a double entry table with descriptive statistics and one with the χ2-test
- We can either report the ‘row’ data e.g. woman reported Y% before and Y% after, with men reporting Y% before and Y% after
OR we can report the ‘colum’ data e.g. woman reported Z% and men reported Z% before, and woman reported Z% and men reported Z% after
Report which is more appropriate - Chi-square test table: report the value, DF and P-value
What is the golden rule when comparing results of a pearsons chi-square test?
NEVER compare percentages which add up to 100%!
What are the three main assumptions we must have before conducting the McNemar test?
- The observations are randomly and independently drawn
- There are at least 25 observations in the discordant cells
- The data are paired
When interpreting the McNemar test table what values do we need to look at?
Need to compare the two percentages that you want to know using ‘% of total’ e.g. The percentage of those who ‘exercised after’ (44.3%) is higher than the percentage of those who ‘exercised before’ (26.0%).
We then use the McNemar test result to see if the finding is significant (this is the p value)
