Statistics fundamentals

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Questions and Answers

Match the verb tenses with their correct usage described in the sentences:

Present Simple = Describes habits or routines that occur regularly. Present Continuous = Describes actions happening right now or around the present time.

Match the words with their appropriate use depending on meaning:

See = To perceive with the eyes; to understand or realize. Wear = To have clothing or accessories on one's body. Hot = Having a high degree of heat or a high temperature. Cold = Having a low degree of heat or a low temperature.

Match the actions to their implied setting

Getting on a plane = Airport departure gate Wearing a coat and scarf = Windy climate Wearing a short skirt = Warm weather Hanging up = Ending a conversation

Match the question to the correct verb tense:

<code>Does it often rain in the winter?</code> = Present Simple as it is talking about general routines. <code>Where do you live?</code> = Present Simple because it's a consistent situation. <code>What are you doing now?</code> = Present Continuous as the action is happening now. <code>Is she going to school on her bike today?</code> = Present Continuous to talk about things that are currently in progress. Signup and view all the answers

Match the clothing to weather:

Boots = Winter Raincoat = Rainy Short Skirt = Hot Coat = Cold Signup and view all the answers

Match the usage to the sentence:

<code>Are you wearing warm clothes?</code> = Asking about an action happening in the present. <code>It's very cold here.</code> = Describing the current weather conditions. <code>I'm wearing my coat and scarf.</code> = Describing actions happening in the present. <code>I'm only joking. It's a lovely, hot day today in Glasgow.</code> = Describing the weather. Signup and view all the answers

Match the correct clothing item to the time of year:

Winter = Boots Rain = Raincoat Hot day = Blouse Signup and view all the answers

Match the different listening comprehension questions to their topics:

What is the weather like? = The current weather situation. What is Jennifer wearing? = The description of the attire of a person. Which tie hasn't Andrew got? = Identifying a choice from a group of options. What are they wearing/doing? = Description of actions and clothing. Signup and view all the answers

Match the correct uses of speech:

Greeting = <code>Hi, Ann. I'm getting on the plane now.</code> Expression = <code>Can't wait to see you.</code> Agreement = <code>All right!</code> Understanding = <code>Really?</code> Signup and view all the answers

Match the use of verbs to the situations:

Habits or routines = She always wears boots in winter. Actions happening now = She is wearing a raincoat now. Expressing a future arrangement = I'm getting on the plane now. Describing a location = I'm on my way to the airport. Signup and view all the answers

Flashcards

Present Simple

Used for habits, routines, and general truths.

Present Continuous

Used for actions happening now or around now.

Present Continuous tense

Expresses actions currently happening.

Where's Patsy?

A question asking about someone's current location.

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Weather in Glasgow

In Glasgow, the weather is lovely and hot today.

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Study Notes

Data is abundant, and variation is inherent, necessitating statistics.
Statistics involves methods for data collection, summarization, analysis, and inference.

Types of Data

Numerical data can be continuous or discrete.
Continuous data takes any value within a range, like height or temperature.
Discrete data involves integer values, like the number of pregnancies.
Categorical data can be nominal or ordinal.
Nominal data includes unordered categories like sex or race.
Ordinal data involves ordered categories like pain scales.

Descriptive Statistics

Descriptive statistics summarize and describe the characteristics of a data set.

Central Tendency

Central tendency includes measures like mean, median, and mode.
Mean (Average): Calculated as $\bar{x} = \frac{\sum x_i}{n}$.
Median is the middle value in a dataset.
Mode is the most frequent value.

Measure of Spread

Measures of spread consists of standard deviation, variance, and range.
Range is the difference between the maximum and minimum values.
Interquartile Range is the range between the first and third quartiles.

Statistical Inference

Statistical inference draws conclusions about a population based on sample data.

Hypothesis Testing

Hypothesis testing assesses evidence to support or reject claims about a population.
Null Hypothesis ($H_0$): States no effect or difference.
Alternative Hypothesis ($H_A$): Contradicts the null hypothesis.
P-value: Probability of observing a result as extreme as, or more extreme than, the one observed if the null hypothesis is true.
Significance Level ($\alpha$): Threshold for determining statistical significance (usually 0.05).
Decision: Reject $H_0$ if the p-value is less than or equal to $\alpha$, otherwise, fail to reject $H_0$.
Type I Error (False Positive): Rejecting $H_0$ when it is true.
Type II Error (False Negative): Failing to reject $H_0$ when it is false.

Common Statistical Tests

Various statistical tests exist for different types of data and research questions.

T-tests

T-tests compare means of one or two groups.
Assumptions of t-tests are normality and equal variance.

ANOVA

ANOVA compares means of three or more groups.

Chi-Square Test

Chi-Square Test examines associations between categorical variables.

Regression

Regression examines the relationship between predictor variables and an outcome variable.
Linear and logistic are types of regression analyses.

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