Module 3

Inferential Statistics

Branch of statistics aiming to make statements about a population based on a sample.

Random Sample

A sample that is representative of the population, achieved through random selection.

Population Parameter

A characteristic or measure obtained by using all the data from a population.

Statistic

A characteristic or measure obtained by using data from a sample.

Probability

A measure of how likely an event is to occur, expressed as a number between 0 and 1.

Cumulative Proportion

The sum of proportions up to a specific point in the distribution.

Stochastic Variable

A variable that can take on different values based on chance.

Empirical Rule

States that for a normal distribution, 68% of observations lie within one standard deviation of the mean.

Standard Error

The standard deviation of the sampling distribution.

Sampling Distribution

The distribution of a statistic (like the mean) over many samples drawn from the same population.

Central Limit Theorem

States that the sampling distribution will be approximately normally distributed if the sample size is sufficiently large.

Random Experiment

An experiment where the outcomes are uncertain, such as rolling a die.

Discrete Variable

A quantitative variable with distinct, separate values (like the number of children).

Continuous Variable

A quantitative variable that can take an infinite number of values within a given range (like height or weight).

Probability Distribution

A function that describes the likelihood of obtaining the possible values of a random variable.

Null Hypothesis (H0)

A statement asserting that there is no effect or no difference; it is the default assumption in hypothesis testing.

Alternative Hypothesis (H1)

The statement that indicates the presence of an effect or a difference; what the researcher aims to support.

Level of Significance

The probability threshold for rejecting the null hypothesis, commonly set at 0.05.

Type I Error

Rejecting the null hypothesis when it is actually true.

Type II Error

Failing to reject the null hypothesis when it is actually false.

P-value

The probability of obtaining a result at least as extreme as the one observed, under the assumption that the null hypothesis is true.

Effect Size

A measure of the strength of the relationship between two variables.

T-Distribution

A probability distribution used when estimating population parameters when the sample size is small and/or population variance is unknown.

Standard Normal Distribution

A normal distribution with a mean of 0 and a standard deviation of 1.

Z-score

The number of standard deviations a data point is from the mean of a distribution.

Statistical Test

A method used to determine if the data supports a specific hypothesis.

Hypothesis Testing Steps

1. State null and alternative hypotheses. 2. Determine level of significance. 3. Collect data and perform test. 4. Calculate p-value. 5. State conclusion.

Random Sampling

Selecting a sample in such a way that each member of the population has an equal chance of being included.

Bias

The tendency of a sample statistic to systematically under- or over-estimate a population parameter.

Confidence Interval

A range of values within which we expect a population parameter to fall, with a certain level of confidence.

Sample Mean

The average of a set of observations from a sample, used as an estimate of the population mean.

Descriptive Statistics

Summary statistics that quantitatively describe or summarize features of a dataset.

Normal Distribution

A symmetrical, bell-shaped distribution defined by its mean and standard deviation.

Law of Large Numbers

States that as a sample size increases, the sample mean will get closer to the population mean.

Histogram

A graphical representation of the distribution of numerical data, showing the frequency of data points in intervals.

Quantitative Variable

A variable that can be measured numerically and can take on many values.

Qualitative Variable

A variable that represents categories or groups and has no numerical value.

Sampling Error

The difference between a sample statistic and the actual population parameter due to the sample being only a part of the population.

Graphical Representation

Visual displays of data, such as charts or graphs, used to summarize and analyze data distributions.

Mean

The average value of a set of numbers, calculated by summing all values and dividing by the count.

Median

The middle value of a dataset when ordered from least to greatest.

Mode

The value that appears most frequently in a dataset.

Variance

The measure of how much individual data points differ from the mean of a dataset.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values.

Cumulative Frequency Distribution

A running total of frequencies up to a certain point in the dataset.

Wilcoxon Test

A non-parametric statistical test used to assess whether two related samples come from the same distribution.

t-test

A statistical test used to compare the means of two groups.

ANOVA

Analysis of variance, a statistical method used to compare means among three or more groups.

Chi-Squared Test

A statistical test used to determine if a significant relationship exists between categorical variables.