CHAPTER #2 - spine of statistics

SPINE statistics

• standard error

• parameters

• interval estimates

• null hypothesis significance testing

• estimation

statistical model

• collect data fromt he real world

• test predictions from our hypotheses about that phenomenon

fit

• degree to which statistical model represents the data collected

good fit

• closely resembles reality

moderate fit

• some similarities to reality but some important differences

poor fit

• completely inaccurate

sample

• data from smaller subset of people

the linear model

• we want to predict the values of an outcome variable (Yᵢ) from a predictor variable (Xᵢ)

• use to summarise the relationship between two variables: the b attached to the predictor variable tells us what the model looks like and the intercept locates the models shape

any straight line can be defined by …

• slope of the line

• and point at which the line crosses the vertical axis

positive b₁

• positive relationship

negative b₁

• negative relationship

steep slope

• large value of b

• outcome changes a lot for a small change in the predictor

flat slope

• low b value

intercept

• determines vertical height of the line

• represents the overall level of the outcome variable when predictor variables are zero

parameters

• constants believed to represent some fundamental truth about the variable model

• ‘estimating parameters’ - we want to know what our model might look like in the whole population

sums of squares and variance

• more data points the higher the ss

  • overcome by using the average error rather than the total

    • to compute avg error → divi sums of squares by the number of values used to compute that total

sums of squared error

• how well a model fits the data

• large values relative to the model indicate lack of fit

method of least squares/ordinary least squares

• min. sum of squared errors

likelihood

• output of the probability density function that describes the popu. of scores

estimating parameters

• probability relative to other scores

• score closer to the popu. mean, the likelihood increases → reaches its max value at the population mean

standard error/sem

• how well it represents the population

• average rating = sample mean

• can be calculated by taking the difference of each sample mean and the overall mean → square the differences → add them together → divide by number of samples

  • square root of this value for standard deviation of sample means

sampling variation

• samples vary because they contain different members of the population

sampling distribution

• frequency distribution of sample means

• how representative sample is of the population

central limit theorem

• as sample gets larger (greater than 30) the sampling distribution has a normal distribution with a mean equal to the population mean

confidence interval

• use a sample value as an estimate of a parameter in the population

• boundaries we believe the population will fall

point estimate

• fixating on a single value from the sample

interval estimate

• use sample value as a midpoint

• set a lower and upper limit around it