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Questions and Answers
What are inferential statistics used for?
What are inferential statistics used for?
Inferential statistics use samples to infer properties of the population.
What is the goal of hypothesis testing?
What is the goal of hypothesis testing?
Hypothesis testing compares a hypothesis of interest to one or more alternative hypotheses.
The hypothesis of interest states that there is no relationship between the independent variable and the dependent variable.
The hypothesis of interest states that there is no relationship between the independent variable and the dependent variable.
False
What does the P-value represent?
What does the P-value represent?
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Which of the following statements about Type 1 and Type 2 errors is TRUE?
Which of the following statements about Type 1 and Type 2 errors is TRUE?
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The probability of Type 1 error depends on the chosen alpha value.
The probability of Type 1 error depends on the chosen alpha value.
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Which of these tests is a Nonparametric test?
Which of these tests is a Nonparametric test?
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Parametric tests compare means and variances.
Parametric tests compare means and variances.
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The Kolmogorov Smirnov test can be used to assess whether parametric statistics can be used.
The Kolmogorov Smirnov test can be used to assess whether parametric statistics can be used.
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What type of test looks at the variation within each sample and compares it with the variance between the samples?
What type of test looks at the variation within each sample and compares it with the variance between the samples?
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What does the term 'degrees of freedom' refer to in the context of Chi-Squared tests?
What does the term 'degrees of freedom' refer to in the context of Chi-Squared tests?
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What is the key difference between a One-tailed and Two-tailed t-test?
What is the key difference between a One-tailed and Two-tailed t-test?
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Under normal distribution, 95% of observations are within 1.96 standard deviations of the mean.
Under normal distribution, 95% of observations are within 1.96 standard deviations of the mean.
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What does the one-sample t-test compare?
What does the one-sample t-test compare?
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What does the paired t-test compare?
What does the paired t-test compare?
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What is the primary purpose of ANOVA?
What is the primary purpose of ANOVA?
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ANOVA compares the variability between samples with the variability within samples.
ANOVA compares the variability between samples with the variability within samples.
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What type of ANOVA is used when we are comparing means from more than two samples?
What type of ANOVA is used when we are comparing means from more than two samples?
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What does the F-value represent in ANOVA?
What does the F-value represent in ANOVA?
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What is the Chi-Squared test used for?
What is the Chi-Squared test used for?
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The frequency of an event is the number of times it occurs.
The frequency of an event is the number of times it occurs.
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What is the formula for calculating Chi-Squared?
What is the formula for calculating Chi-Squared?
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Study Notes
Inferential Statistics Overview
- Inferential statistics uses samples to draw conclusions about larger populations.
- It's a tool to understand the underlying nature of phenomena.
- Inferential statistics allows researchers to test hypotheses and determine relationships between variables.
- It enables predictions about populations based on sample data.
Learning Outcomes
- Students will be able to draw reliable conclusions from samples of large populations.
- Students will be able to compare different populations.
- Students will be able to explain when to use various inferential statistical methods.
- Students will be able to perform calculations involved in t-tests and Chi-Squared tests.
Hypothesis Testing
- A formalized method for understanding the world.
- It compares a hypothesis of interest with alternative hypotheses.
- The hypothesis of interest states a specific relationship between variables.
- The null hypothesis states there is no relationship between variables.
Relationship Between Variables
- Correlation coefficients describe the linear relationship between two variables.
- Correlation coefficients range from -1 to 1.
- A value of -1 indicates a strong negative correlation.
- A value of 1 indicates a strong positive correlation.
- A value of 0 indicates no linear correlation.
- Visualizations like scatter plots illustrate the correlation between variables.
Hypothesis Testing (cont.)
- The p-value represents the probability of observing the data if the null hypothesis is true.
- The alpha value is a pre-determined threshold for rejecting the null hypothesis.
- A p-value less than alpha indicates rejection of the null hypothesis.
- Common alpha values are 0.05 and 0.01.
Hypothesis Testing (cont.)
- Type 1 error (false positive): rejecting a true null hypothesis.
- Type 2 error (false negative): failing to reject a false null hypothesis.
- Alpha value influences the probability of a Type 1 error.
- Statistical power relies on sample size and effect size to avoid Type 2 errors.
Tests of Significance
- Nonparametric: Chi-Square, Fisher's exact test - Analyse relationship between categorical variables
- Parametric: T-test (paired, unpaired), ANOVA, Pearson's Correlation, Linear Regression - Used when data are normally distributed - Compare means/variances in groups
Parametric Tests
- Used when data are normally distributed.
- Compare means and variances.
- The Kolmogorov-Smirnov test assesses normality of data for parametric use.
Commonly Used Parametric T-Tests
- Used to compare means in two groups.
- Dependent variable: interval/ratio.
- Independent variable: nominal/ordinal (with two groups).
- Associated plots: Bar, Box, Violin.
Commonly Used Parametric ANOVA
- Used to compare means in more than two groups.
- Dependent variable: interval/ratio.
- Independent variable: nominal/ordinal (with more than two groups).
- Associated plots: Bar, Box, Violin.
Commonly Used Parametric Correlation
- Measures the dependence between two variables.
- Variables: interval/ratio.
- Associated plot: Scatter Plot
Commonly Used Parametric Regression
- Measures dependence between two or more variables.
- Dependent variable: interval/ratio.
- Independent variables: of any type.
- Associated plots: Scatter Plot, Box Plot.
Non-Parametric Tests
- Used when data don't satisfy parametric test requirements.
- Typically compare medians.
- Rank data instead of raw values.
Specific Non-parametric and Parametric tests and conditions
- Independent measures, 2 groups: Mann-Whitney test(non), independent measures t-test (param)
- Independent measures, >2 groups: Kruskal-Wallis test(non), one way independent measure ANOVA(param)
- Repeated measures, 2 conditions: Wilcoxon test (non), matched pair t-test(param)
T-Tests
- Key tool for comparing means in biological systems.
- Experimental design controls variables.
- Tests the probability that samples come from one population with a single mean.
- T-values indicate significance levels.
T-test Tables
- T-values in tables show significance level differences between two means based on sample size and t-score.
- Reject the null hypothesis if the calculated t-value is greater than the critical value in the table.
Example: T-test application
- Comparison of egg masses from different species.
- Calculated t-score greater than critical value (significance level).
One-tailed vs Two-tailed Tests
- One-tailed: Hypothesis predicts direction of effect.
- Two-tailed: Hypothesis doesn't specify direction of effect.
One-Sample t-test
- Compares a single sample mean with a known population mean.
- Calculates how many standard errors the sample mean deviates from the population mean.
Paired t-test
- Compares means of the same variable measured under different conditions or at different times.
- Divides the mean difference by the standard error of the difference.
Unpaired t-test
- Compares means of the same variable in two different samples.
- Divides the difference between sample means by the standard error of the difference.
Analysis of Variance (ANOVA)
- Compares multiple samples, avoiding multiple comparisons errors.
- Compares mean variation within samples to mean variation between samples.
One-way ANOVA
- Compares means of more than two samples.
Repeated Measures ANOVA
- For repeated measurements on the same sampling unit.
F-value in ANOVA
- ANOVA test statistic that compares between-sample and within-sample variations.
- Ratio of mean square between groups to mean square within groups.
Chi-squared Test
- Compares frequencies between expected and observed values of nominal data.
Calculating Chi Squared
- Formula for calculating Chi-squared:
x² = ∑ ( (O−E)² / E )where:- O = observed frequencies
- E = expected frequencies
- ∑ = sum of
Chi-squared Significance Level
- The significance level in Chi-squared tests depends on degrees of freedom.
- Degrees of freedom = (number of rows - 1) * (number of columns - 1)
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Description
This quiz covers the fundamentals of inferential statistics, including hypothesis testing and the utility of sample data to draw conclusions about populations. Students will learn to apply various inferential methods and perform necessary calculations. Dive in to improve your understanding of statistical relationships and predictions.
