NHST

# Null Hypothesis Significance Testing (NHST)
## Professor Andy Field

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???

Music: Black Crown Initiate A Great Mistake

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# The SPINE of statistics

## 5 Key concepts

* **S**tandard error

* **P**arameters

* **I**nterval estimates
 
* **N**ull hypothesis significance testing (NHST)

* **E**stimation

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![:scale 83%](media/spine_content_map.png)
???

We've seen this map of the process of fitting models before

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class: center

![:scale 83%](media/spine_lec_03.png)

???

Today we focus on NHST.

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#  Learning outcomes

* Null hypothesis significance testing (NHST)
  - Understand the process of significance testing parameters
  - Understand what a *p*-value represents
  - Understand what a *p*-value does NOT represent

* Problems with NHST
  - Be able to articulate the limitations of NHST

* Understand what an effect size is and how it should be used to contextualise significance tests

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class: center, middle
background-image: none

![:scale 50%](media/dsr2_fig_03_16_nhst.png)

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.ong_dk[
$$
`\begin{aligned}
\text{ringing}_i &= \hat{b}_0 + \hat{b}_1\text{volume}_{i} + e_i
\end{aligned}`
$$
]

![](nhst_ais_files/figure-html/unnamed-chunk-27-1.png)

---
class: center

.ong_dk[
$$
`\begin{aligned}
\text{ringing}_i &= \hat{b}_0 + \hat{b}_1\text{volume}_{i} + e_i
\end{aligned}`
$$
]

![](nhst_ais_files/figure-html/unnamed-chunk-28-1.png)

---
class: center

.ong_dk[
$$
`\begin{aligned}
\text{ringing}_i &= \hat{b}_0 + \hat{b}_1\text{musician}_{i} + e_i
\end{aligned}`
$$
]

![](nhst_ais_files/figure-html/unnamed-chunk-29-1.png)

---
class: center

.ong_dk[
$$
`\begin{aligned}
\text{ringing}_i &= \hat{b}_0 + \hat{b}_1\text{musician}_{i} + e_i
\end{aligned}`
$$
]

![](nhst_ais_files/figure-html/unnamed-chunk-30-1.png)
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# The long-run probability of the test statistic

.pull-left[
* Parameters represent effects:
  - Relationships between variables
  - Differences between means
* Parameters reflect hypotheses:
  - `$H_0$`: `$b = 0$` or `$b_1 = b_2$`
  - `$H_1$`: `$b \ne 0$` or `$b_1 \ne b_2$`
* All parameters have an associated sampling distribution
  - For any parameter, we can work out the probability of getting at least the value we have if the null hypothesis is true (e.g., if `$b = 0$`, or `$b_1 \ne b_2$`)
  - *p* < 0.05 is typically used as a threshold for ‘significance’
]

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# The long-run probability of the test statistic

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# What is a *p*-value?

![:scale 50%](media/alice_nightingale.png)

H<sub>0</sub>: Alice does not want to date Zach

H<sub>1</sub>: Alice wants to date Zach

]
]

--
.pull-right[
.center[
## Test statistic

![:scale 50%](media/zach_slade.png)

Humour rating = 5
]
]

???

Alice and Zach met in their college library when they were teenagers. Imagine he’d been curious to know whether Alice would date him.
H0 = she doesn’t
H1 =  she does.
How does he find out which is the case? Collect data.

We know from work by Ha et al., that teenage girls rate humour highly as a characteristic 
Imagine that the college is really weird and had a dating system. Every day you’re sent a picture of someone you know, and you’re asked to rate them along the same dimensions as in the Ha study (kindness, attractiveness, humour, ambition etc.) and then you’re asked whether you’d date the person. Alice is shy and studious. She has diligently rated hundreds of people but for every one of them she has responded that she doesn’t want to date them. In other words, we have a bunch of information about the ratings she gives *when the null hypothesis is true*.

Then, one day, Alice rates Zach.

Zach discovers that she gives him a 5/10 on humour. This seems low. Knowing how important humour is in potential partners he feels dejected. The problem is that he has no context for his ‘test statistic. A p-value provides this context.

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# What is a *p*-value?

]