Statistical formulas

Question 1

ANOVA
Analysis of Variance 

Answer 1

Let’s say you have water, juice, coffee and you want to see their reaction time . Because there are three groups you need to use analysis of variance. Null hypothesis said the mean, for all the reaction time is the same. To test you need to measure variation with each groupand the Variation between each groups.

Analysis of Variance (ANOVA) is a statistical method used to compare the means of three or more samples to determine if at least one of the sample means significantly differs from the others. It tests the null hypothesis that all group means are equal versus the alternative hypothesis that at least one group mean is different. ANOVA helps to assess the impact of one or more factors by comparing the variance within groups to the variance between groups, providing insights into the relationships among group means.

Question 2

Standard deviation

Answer 2

standard deviation is a statistical measure. Standard deviation is used to quantify the amount of variation or dispersion of a set of data values. It is a measure of how spread out the numbers in a data set are around the mean (average) of the set.

In simpler terms, if the standard deviation is small, it means that the data points are close to the mean, indicating less variability within the data set. Conversely, a large standard deviation indicates that the data points are spread out over a wider range of values, showing higher variability.

The standard deviation is particularly useful in comparing the spread of different data sets or understanding the reliability of the data. It plays a crucial role in finance, science, engineering, and many other fields that rely on statistical analysis

Question 3

What is a Scatterplots?

Answer 3

Scatterplots are a type of graph used in statistics to display values for typically two variables for a set of data. The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. Scatter plots are used to observe and show relationships between two numeric variables.

The main purposes of a scatter plot include: 1. Identifying the type of relationship between two variables. This relationship can be linear, nonlinear, or nonexistent. A linear relationship appears as a roughly straight line of points; a nonlinear relationship appears as a curve; and a nonexistent relationship results in a random distribution of points.
2. Determining the strength of the relationship between the variables. In a scatter plot, a clear pattern indicates a strong relationship, whereas a more dispersed pattern suggests a weaker relationship.
3. Spotting outliers, unusual observations, or anomalies in the data that do not fit the general pattern.

Question 4

What is a quantitative data?

Answer 4

It is numeric data. Discrete (counting) whole numbers, like 5 cats 8 people.
Continuous: (measurements)  distance, hight  speed
In the context of my study, averaging the responses to the SWLS questions is an example of quantitative data, because it results in a numeric value that represents the level of well-being. I can perform mathematical calculations with this data:

Question 5

What is ordinal data?

Answer 5

Is a type of categorical data that has a rank, order, named qualities.
Example: small, medium large: grades, D C B A: fan low, medium high. Ordinal data has natural order. Example. small is smaller then medium but large is bigger then medium. They have natural order in them and we can naturally sort them out. Ordinal data is powerful then mathematical data.

Question 6

Qualitative data

Answer 6

Is a data that is descriptive data based on observations. It involves 5 senses to see (color), to feel (soft), taste ( food tastes good), hear( volume low), smell (good or bad)

Question 7

Spearman’s correlation

Answer 7

To test the hypothesis that there is a positive correlation between the frequency of prayer and service attendance, and subjective well-being.spearman’s correlation you can analyze both ordinal and continuous data.
Pearson’s requires only continuous data which in our data collection will not be enough.