Week 11 Flashcards
What kind of data is used in parametric tests?
Numerical data (interval or ratio).
What kind of data is used in non-parametric tests?
Categorical data (nominal or ordinal).
Parametric tests normally make assumptions, what are they?
Population parameters such as mean and normality of distribution.
List the 3 main reasons for using non-parametric tests.
- Numerical scores violate assumptions of mean and normality of distribution (unless solved with sample information).
- High level of variance in numerical data (converting numerical to ordinal data)
- Grouping is sometimes more convenient (scores, participants etc).
What does a Chi-square goodness-to-fit test measure?
Uses sample data to determine how well a sample proportions fit the population proportions based on the null hypothesis. (How well ƒₒ fits with ƒₑ)
What are the TWO hypothesises for a Chi-square goodness-to-fit test.
- Equal proportions/No preference (50/50 or 33.33/33.33/33.33 etc).
- No difference (to population proportions).
Is there a alternative hypothesis for a Chi-square goodness-to-fit test?
No.
What is observed frequency in a Chi-square goodness-to-fit test?
The data observed in the sample.
What is expected frequency in a Chi-square goodness-to-fit test?
What the distribution is expected to look like.
What symbol is used to represent expected frequency in Chi-squared tests?
ƒₑ
What symbol is used to represent observed frequency in Chi- squared tests?
ƒₒ
What symbol is used to represent Chi-squared?
𝜒²
What is the formula for Chi-squared?
𝜒² = ∑(ƒₒ-ƒₑ)² / ƒₑ
What is Chi-squared?
A theoretical, positively skewed distribution consisting of all possible random samples that would exist if the null hypothesis is true.
(Similar to a t-test distribution).
What does the Chi-squared of independence test measure?
Determines if a relationship exists between two categorical variables.
What is the null hypothesis for a Chi-squared of independence test?
X is NOT an independent variable for Y.
What is the alternative hypothesis for a Chi-squared of independence test?
X IS an independent variable for Y.
There is a relationship between the variables
How do you calculate ƒₑ for a Chi-squared of independence test?
ƒₑ = ƒ꜀ƒᵣ/n
What does ƒ꜀ represent?
Column frequency.
What does ƒᵣ represent?
Row frequency.
How do you calculate ƒₑ for a Chi-squared goodness to fit test?
ƒₑ = pn
proportion times sample
How do you calculate the df in a Chi-squared of independence tests?
df = (R-1)(C-1)
(Row sample size - 1 times column sample size -1
What is risk in statistics?
The probability that an event occurs.
What is a basic calculation of risk in words? (hint: it is the equation for probability).
Number of outcomes classified as A divided by the total number of outcomes.
What is odds in statistic?
The number of times that the event will occur divided by the number of times that the event will not occur.
What is relative risk in statistics?
Comparing the risk of the same event between two groups.
What is the calculation of relative risk in words?
Risk that the event occurs for group 1 divided by risk that the event occurs for group 2.
What is the calculation of an odds ratio in words?
Odds of an outcome for group 1 divided by odds of an outcome for group 2.
How to do you preform relative risk and odds ratios in SPSS?
- Analyse.
- Descriptive statistics.
- Crosstabs.
How do you calculate the df in a Chi-squared goodness to fit tests?
df = number of categories - 1
What assumptions do nonparametric tests make?
- Do not require the populations to have normal distributions.
- Can be performed on data measured on any scale.
- Make few, if any assumptions about the populations.
How does the difference between ƒₒ and ƒₑ influence the outcome of a chi-square test?
The larger the difference, the larger the value of chi-square, and the greater the likelihood of rejecting the null hypothesis.
What happens to the critical value for a chi-square test if the size of the sample is increased?
The critical value depends on the number of categories, not the sample size.
For a fixed level of significance, the critical value for the chi-square will increase as the ____ increases?
Degree of freedom.
