Scientific Foundations Of Psychology Week 10 - Part One

Frequentist View

Defines probability as a long-run frequency

• Even if you get 6 heads in a row, if you continue to flip a count, eventually the proportion of heads will eventually converge to 50%

Desirable Characteristics Of Frequentist Definition

• Objective: Necessarily grounded in the world

• Unambiguous: As two people watch the sequence and try to come up with a probability, they will usually end up with the same answer

Undesirable Characteristics Of Frequentist Definitions

• Infinite sequences don’t exist

• Narrow scope

• Forbids making probability statements about single event

Elementary Event

An outcome is one of these events out of the probabilities/options

Sample Space

Set of all possible events in a probability

Non-Elementary Events

An event that is possible but isn’t apart of specifically measured events

• If we measure for how often someone wears trousers, and then someone wears jeans

Null Hypothesis Significance Testing

Statistical method used to evaluate whether observed results in study are significantly significant or whether they have could occurred by chance

• Compare normal data with null hypothesis

Research Hypothesis

Involves making substantive, testable scientific claim

Statustical Hypothesis

Must be mathematically precise and correspond to specific claims about the characteristics of the data generating mechanism

• Clear relationship to the substance research hypothesis that you care about

Null Hypothesis

The opposite to what hypothesis the scientist has created

Alternative Hypothesis

A hypothesis that is almost an in between the null and the normal hypothesis

• Basically, by accepting the alternative hypothesis, this means that it actually allows our hypothesis/idea to be confirmed

Trial Of Null Hypothesis

Null hypothesis is defendant, researcher is the prosecutor and statistical test is the judge

• Goal is to maximise the chance the data will yield a conviction for the crime of being false

Type One Error

If the null hypothesis is rejected when it is correct/valid

Type Two Error

The null hypothesis is retained when it is false

Critical Region

Corresponds to those values that would lead us to reject the null hypothesis

• Most extreme values (tails of results)

Ways To Find Critical Region

• X should be very big or very small in order to reject the null hypothesis

• If the null hypothesis is true, the sampling distributions of X is binomial

• If alpha = .05, the critical region must cover 5% of this sampling distribution

How To Understand Critical Region

If we chose critical region that covers 20% and the null hypothesis is true, rejecting the null hypothesis leads to a 20% chance of incorrectly rejecting null hypothesis

What Does It Mean When We Reject The Null Hypothesis?

The results are statistically significant

Two-Sided Hypothesis

Alternative hypothesis covers the area on both “sides” of the null hypothesis and covers both tails of sampling distribution

One-Sided Test

Critical region only covers on tail of the sampling distribution

Values Of Alpha And Their Meanings

• 0.05: Reject Null

• 0.04: Reject Null

• 0.03: Reject Null

• 0.02: Accept Null

• 0.01: Accept Null

P Value True Definition

Smallest type one error rate that you would be willing to tolerate if you want to reejct the hypothesis

• P value of 0.21 means there is a 2.1% error rate i have to tolerate

• Its up to us on how to interpret the value and how willing we are to tolerate the rate of error

• tells the likelihood of getting your result if there is no difference in that population

Good Critical Region

almost always corresponds to those values of the test statistic that are least likely to be observed if the null hypothesis is true

• If this rule is true, then we can define the p-value as the probability that we would have observed a test statistic that is at least as extreme as the one we actually did get (basically the p-value gives us a probability that we will get the answers that we actually achieved and determines if they are real)

Mistake With P Value

The mistake is that they believe that the p value is the “probability that the null hypothesis is true”

Issue With P Value

Individuals argue that we should report the actual p-value and allow readers to determine whether it is an acceptable type 1 error rate

P Value significance Results

if p < 0.05, the results are real and confirmed

If p > 0.05, the probability of the result being chance is great

Proposed Solutions For P Value

• Dont report the exact p value as it leaves too much room for interpretation

• Furthermore, scientists can report the p value as .05, .01 or .001, which softens decision rule since p<.01 implies data meets stronger evidental standard than p<0.5 would.

P Value and Alpha Association

• if the P value is less than the alpha, we reject the null hypothesis

• If the P Valye is more than the alpha, we accept the null hypothesis

Independent Samples T-Test

Variability between groups and the variability within groups

• the bigger the T value, the more tou move along the standard distribution and the rarer it gets

Variability Between Groups

How well people respond to one treatment in comparison to another (some treatments/interventions work better than others)

• signal

Variability Within Groups

How well a number of people receiving one type of treatment respond (Everyone’s responses are usually different, regardless of what the intervention is)

• Noise

Between subjects Variability

Dufference between the mean of one group and the mean of another

Difference Between Z Score And T-Test

• Z score is where a person fits in the wider world

• T-Test is about where a group fits in a wider world

What Means Of The Groups Are Important?

• The larger the mean between the groups, the more plausible the results are

• If the difference in the mean is larger than the shared ratios, it means the results are more likley to support the hypothesis

What Happens If A Score Falls Within 95% Of Scores

Likely that the score occurred due to random chance and not because of the experiment