A t-test is a hypothesis test for statistical significance between two sample means based on t-statistics. Before it can be conducted, it must meet the conditions for inference.

conditions for inference (t-test)

To use t-statistics, you have to meet three conditions just like the conditions for inference used in z-score.

• random sampling
• normal (sample size larger than 30, or if original distribution is confirmed as roughly symmetric about the mean)
• Independence

use a z-statistic to find a p-value

Begin by finding a \(t\) statistic. Remember that:

For an operator \(T \in \mathcal{L}(V)\), \(T^{n}\) would make sense. Instead of writing \(TTT\dots\), then, we just write \(T^{n}\).

constituents

• operator \(T \in \mathcal{L}(V)\)

requirements

• \(T^{m} = T \dots T\)

additional information

\(T^{0}\)

\begin{equation} T^{0} := I \in \mathcal{L}(V) \end{equation}

\(T^{-1}\)

\begin{equation} T^{-m} = (T^{-1})^{m} \end{equation}

if \(T\) is invertable

usual rules of squaring

\begin{equation} \begin{cases} T^{m}T^{n} = T^{m+n} \\ (T^{m})^{n} = T^{mn} \end{cases} \end{equation}

This can be shown by counting the number of times \(T\) is repeated by writing each \(T^{m}\) out.

Moved much of this to Drafts instead

• phonbank: poor articulation

• disfluent kids

• late talkers

• Write a review about ASR benchmark methods

  • REV would be our benchmark
    • What corpora we use?
    • Has anyone used disordered speech?
    • Or really seriously accented speech vis a vi CORALL (how was CORALL sampled?)
  • What samples? How do we sample? What are the benchmarks?

• ASR model + WER

• tildes and noprompt swapped

• WER

• missing words

Lit Survey

Pipeline

Segmentation