Topic 1: Statistical Analysis
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I.B. students testing out of SL Biology need to know a few things from topic 1 about statistical analysis
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Estimation involves making inferences about a population based on a sample. An estimator is a statistic used to estimate unknown population parameters, and the estimate is the computed value. A good estimator is unbiased, efficient, and consistent. Confidence intervals provide a range of values that are likely to contain the true population parameter, depending on the sample size, confidence level, and variability of the data. Both confidence intervals and p-values provide important information but confidence intervals also convey the magnitude and strength of an effect.
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- The null hypothesis states there is no difference between what is observed and what is expected. The alternative hypothesis specifies an alternative statement.
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This document discusses comparative statistics and statistical tests used to compare groups. It describes how comparative tests usually aim to test for differences between groups rather than similarities. The null hypothesis states there is no difference between groups, while the alternative hypothesis predicts a difference. Statistical tests determine whether to reject the null hypothesis based on the likelihood the results are due to chance. P-values indicate whether results are extreme enough to reject the null hypothesis. Confidence intervals provide information about expected values in the overall population based on study results. The document outlines different types of comparative tests that are appropriate depending on the variables and populations being compared, such as independent or paired groups.
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- The null hypothesis states there is no difference between what is observed and what is expected. The alternative hypothesis specifies an alternative statement.
- Steps in hypothesis testing include formulating the hypotheses, selecting a statistical test, collecting data, determining critical values and probabilities, and deciding whether to reject or fail to reject the null hypothesis.
- Parametric tests assume a known distribution while nonparametric tests make no assumptions. Common tests mentioned include t-tests, z-tests, F-tests, chi-square tests, and rank correlation tests.
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Descriptive statistics are used to analyze and summarize data. There are two types of descriptive measures: measures of central tendency that describe a typical response like the mode, median, and mean; and measures of variability that reveal the typical difference between values like the range and standard deviation. Statistical analysis can be descriptive to summarize data, inferential to make conclusions about a population, differences to compare groups, associative to determine relationships, or predictive to forecast events. Data coding and a code book are used to identify codes for questionnaire responses.
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- Sample size, population size, and response distribution (how answers are split) all impact the required sample size to achieve a given confidence level and interval. Higher confidence or lower intervals require larger samples.
- For a population of 20,000, with a 50-50 response split, and 95% confidence level, the required sample size is 377 people.
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- Whether tests are one-tailed or two-tailed depending on if the alternative hypothesis specifies a directional difference.
- Type I and Type II errors, with Type I errors occurring when the null hypothesis is incorrectly rejected and Type II errors occurring when it is incorrectly accepted.
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For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study.
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This document discusses hypothesis testing and the key concepts involved, including:
- The difference between the null and alternative hypotheses, with the null hypothesis representing the hypothesis being tested.
- Whether tests are one-tailed or two-tailed depending on if the alternative hypothesis specifies a directional difference.
- Type I and Type II errors, with Type I errors occurring when the null hypothesis is incorrectly rejected and Type II errors occurring when it is incorrectly accepted.
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Similar to Topic 1: Statistical Analysis
1 statistical analysis notes
This document discusses key concepts in statistical analysis:
1) Error bars represent the variability in data and can show the range or standard deviation. The standard deviation summarizes how data values are spread around the mean, with 68% of values within one standard deviation.
2) The standard deviation is useful for comparing means and spreads between samples. Larger differences in means and standard deviations between samples indicate they are less likely from the same population.
3) A t-test measures the overlap between two data sets and determines if their differences are statistically significant or likely due to chance. A significance level of 5% is commonly used, below which the null hypothesis that sets are the same is rejected.
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2. chapter ii(analyz)
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1. It describes four scales of measurement (nominal, ordinal, interval, ratio) and warns against using statistics inappropriate for the scale of data.
2. It distinguishes between parametric and non-parametric statistics, descriptive and inferential statistics, and the types of variables and analyses.
3. It explains important statistical concepts like hypotheses, one-tailed and two-tailed tests, distributions, significance, and avoiding type I and II errors in hypothesis testing.
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ststs nw.pptx
Statistical concepts and their applications in various fields:
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- Descriptive statistics summarize data through measures of central tendency (mean, median, mode) and variability (range, standard deviation).
- Inferential statistics test hypotheses and make estimates about populations based on samples.
- Biostatistics is applied in community medicine, public health, cancer research, pharmacology, and demography to study disease trends, treatment effectiveness, and population attributes. It is also used in advanced biomedical technologies and ecology.
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1. complete stats notes
1) Statistics is the science of collecting, analyzing, and drawing conclusions from data. It is used to understand populations based on samples since directly measuring entire populations is often impossible.
2) There are two main types of data: qualitative data which relates to descriptive characteristics, and quantitative data which can be expressed numerically. Common statistical analyses include calculating the mean, standard deviation, and using t-tests, ANOVA, correlation, and chi-squared tests.
3) Statistical analyses allow researchers to determine uncertainties in measurements, compare groups, identify relationships between variables, and assess whether observed differences are likely due to chance or a factor being studied. Key concepts include null and alternative hypotheses, p-values, and effect size.
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The t-distribution is a probability distribution used for statistical analysis when sample sizes are small or population standard deviations are unknown. It is similar to the normal distribution but with heavier tails, accounting for more uncertainty. The t-distribution is applied in hypothesis testing and constructing confidence intervals to make inferences about population means based on small samples. Its shape depends on degrees of freedom which reflects sample size information. It assumes data is normally distributed and population variance is unknown.
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Topic 1: Statistical Analysis
- 2. Normal Distribution Mean in center
- 3. Standard Deviation • Used to assess how far the values are spread above and below the mean • 68% of values lie within one standard deviation • 95% of values lie within two standard deviations • Can be used to determine whether the difference between two means is significant
- 4. Error Bars • Bars on graphs extending above and below the mean value • Show the variability of data • Can be used to show the range of data or the standard deviation
- 5. The t-Test • Can be used to find out whether there is a significant difference between the means of two populations • If the probability of it being due to random variation is 5% or less it is considered statistically significant • The larger the difference between two means, the larger t is • The larger the standard deviations, the smaller t is
- 6. Correlation and Cause • The existence of a correlation between two variables does not indicate and causal relationship between the two