Stats tester plus

### Features of this app ###

1. By using Stats tester plus, you can perform some statistics tests by an easy operation.
2. Since one sample group (multiple data) is entered in one window, it is very easy to add or modify the data.
3. Built-in numeric keypads with telephone layout and calculator layout.
4. Unlike other test apps, not only final conclusions such as p-values, but also intermediate results are shown.
5. Input data and all output screen can be recorded by sharing (mail, memo). No need to take notes on paper.
6. You can import data by copy / paste from apps such as Numbers, Excel, Memo, etc.

## how to use ##

Each test screen has [Help], [Example], [Graph], [Calc], [Clear] and [Share] buttons.

### Statistics methods ###

A. Basic Statistics (Mean,SD,Median, etc.)
1. Mean, SD, Skewness, Kurtosis, etc.
( Means (Arithmetic, Geometric and Harmonic), Standard Deviation、Standard Error、Confidence interval (CI, 95 and 99%), Variance, Unbiased variance, Coefficient of variation (%CV), Skewness, Kurtosis)
2. Median, Range, Quartiles and Boxplot
(Median, Maximum, Minimum, Quartiles, Quartile Deviation, Boxplot Graph)

B. Test for Mean,Variance,etc. (Parametric)
1. One-Sample t-Test (to Compared Mean)
2. Two-Sample t-Test (Student's and Welch's t-Tests)
3. Paired t-Test (Paired Sample)
4. F-Test of Variance for Two Samples
5. Levene Test of Variance for Multiple Samples
6. One-Way Analysis of Variance (ANOVA)
7. Multiple t-Test with Bonferroni Correction

C. Test for Median, etc. (Nonparametric)
1. Mann-Whitney U Test (Two Samples)
2. Median Test (Two Samples)
3. Wilcoxon Signed Rank Test (Paired Sample)
4. Kruskal-Wallis Test & Multiple Comparisons (by Bonferroni Correction)

D. Test for Proportion
1. Sign Test (Paired Sample)
2. Binomial Test [Exact Method] (One-Sample Proportion Test)
3. Binomial Test [Approx Method] (One-Sample Proportion Test)
4. Two-Sample Proportion Test [Approx. Method]

E. Test for Frequency
1. Chi-Square Test (Goodness of Fit)
2. Chi-Square Test (2x2, Independence)
3. Chi-Square Test (mxn, Independence)
4. McNemar's Test (Chi-Square Test for Paired Sample)
5. Fisher's Exact Test (2x2)

F. Test for Correlation
1. Linear Regression and Test for Pearson Correlation Coefficient
2. Test for Differences in Correlation Coefficients (One Sample)
3. Test for Differences in Correlation Coefficients (Two Samples)
4. Spearman Rank Correlation Test

G. Other (Normality Test)
1. Shapiro-Wilk Test (Normality) and Q-Q Plot

## Appendix ##

Sample output of F-1. [Linear Regression and Test for Pearson Correlation Coefficient]
===============================
[Input data: pairs (X,Y)]
X, Y
1: 1, 5
2: 4, 8
3: 4, 7
4: 6, 10
5: 8, 11

n = 5

[Correlation coefficient]
r = 0.9798012

[Regression coefficient (a and b)]
y = a + bx
a = 4.0735292 (intercept)
b = 0.89705884 (slope)

Coefficient of determination :
2
R = 0.9600103

== Test for Correlation coefficient ==

Ho (Null hypothesis) : ρ = 0 (ρ:rho)
Ha (Alternative hypo) : ρ ≠ 0
ρ: Correlation coefficient of population

Sample correlation coefficient:
r = 0.9798012
Degree of freedom:
df = 3
Test statistic:
to = 8.486422

p = 0.003436 ** (2 tails)
→ Ho is rejected.(p＜0.01)
===============================

### Acknowledgment ###

The iOs Chart library distributed under the Apache 2.0 license was utilized to make graphs.
https://github.com/danielgindi/Charts
http://www.apache.org/licenses/LICENSE-2.0.html